BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pavlos Motakis (UIUC) DTSTART:20200410T140000Z DTEND:20200410T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/1 DESCRIPTION:Title: Coarse Universality\nby Pavlos Motakis (UIUC) as part of Banach spaces webinars\n\n\nAbstract\nThe Bourgain index is a tool that can be u sed to show that if a separable Banach space contains isomorphic copies of all members of a class $C$ then it must contain isomorphic copies of all separable Banach spaces. This can be applied\, e.g.\, to the class $C$ of separable reflexive spaces. Notably\, the embedding of each member of $C$ does not witness the universality of $X$. We investigate a natural coarse analogue of this index which can be used\, e.g.\, to show that a separable metric space that contains coarse copies of all members in certain “sma ll" classes of metric spaces $C$ then $X$ contains a coarse copy of $c_0$ and thus of all separable metric spaces.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Ostrovskii (St. John's) DTSTART:20200417T140000Z DTEND:20200417T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/2 DESCRIPTION:Title: Transportation cost spaces\, also known as Arens-Eells spaces\, Lip schitz-free spaces\, Wasserstein 1 spaces\, etc.\nby Mikhail Ostrovski i (St. John's) as part of Banach spaces webinars\n\n\nAbstract\nAfter a br ief introduction I shall talk about $\\ell_1$-subspaces in transportation cost spaces. Results presented in this talk\, mentioned in it\, or related to it\, can be found in joint papers with Stephen Dilworth\, Seychelle Kh an\, Denka Kutzarova\, Mutasim Mim\, and Sofiya Ostrovska\, see \n
\n\n Lipschitz free spaces on finite metric spaces\n
\n\nGen eralized transportation cost spaces\n
\n\nIsometric copies of $\\ell^n_{\\infty}$ and $\\ell_1^n$ in transportation cost spaces on finite metric spaces\n
\n\nOn relations between transportation co st spaces and $L_1$\n LOCATION:https://researchseminars.org/talk/BanachWebinars/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Tomasz Kania (Czech Academy of Sciences) DTSTART:20200424T140000Z DTEND:20200424T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/3 DESCRIPTION:Title: Quantifying Kottman's constant\nby Tomasz Kania (Czech Academy of Sciences) as part of Banach spaces webinars\n\n\nAbstract\nKottman's co nstant\, $K(X)$\, of a Banach space $X$ is the supremum over those $d>0$ f or which the unit sphere of $X$ contains a $d$-separated sequence. It is k nown that $K(X)>1$ for every infinite-dimensional space $X$ (the Elton–O dell theorem). I will present certain estimates related to interpolation s paces\, twisted sums\, and other classes of Banach spaces $X$ concerning t he isomorphic Kottman constant\, defined as the infimum of $K(Y)$\, where $Y$ ranges over all renormings of $X$. \nI will also comment on other rela ted constants (such as the disjoint one defined for Banach lattices) and t heir symmetric analogs.\n\n\n\nThis talk is based on papers with J. M. F. Castillo\, M\, González\, P. L. Papini (PAMS 2020+) and P. Hájek\, T. Ru sso (JFA 2018).\n LOCATION:https://researchseminars.org/talk/BanachWebinars/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Freeman (St Louis University) DTSTART:20200501T140000Z DTEND:20200501T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/4 DESCRIPTION:Title: A Schauder basis for $L_2$ consisting of non-negative functions< /a>\nby Daniel Freeman (St Louis University) as part of Banach spaces webi nars\n\n\nAbstract\nWe will discuss what coordinate systems can be created for $L_p(\\R)$ using only non-negative functions with $1 \\leq p<\\infty$ . In particular\, we will describe the construction of a Schauder basis fo r $L_2(\\mathbb R)$ consisting of only non-negative functions. We will con clude with a discussion of some related open problems. \n\nThis is joint w ork with Alex Powell and Mitchell Taylor.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Gartland (UIUC) DTSTART:20200508T140000Z DTEND:20200508T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/5 DESCRIPTION:Title: Lipschitz free spaces over locally compact metric spaces\nby Ch ris Gartland (UIUC) as part of Banach spaces webinars\n\n\nAbstract\nThe t alk is generally about questions of local-to-global phenomena in metric an d Banach space theory. There are two motivating questions: Let X be a comp lete\, locally compact metric space. (1) If every compact subset of X biLi pschitz embeds into a Banach space with the Radon-Nikodym property\, is th e same true of X? (2) If the Lipschitz free space over K has the Radon-Nik odym property for every compact subset K of X\, is the same true for the L ipschitz free space over X? We will first overview the theory of non-biLip schitz embeddability of metric spaces into Banach spaces with the Radon-Ni kodym property\, and then discuss an idea developed in an attempt to answe r (2). We will show how this idea may be used to answer modified versions of (2) when the Radon-Nikodym property is replaced by the Schur or approxi mation property.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Gideon Schechtman (Weizmann Institute of Science) DTSTART:20200515T140000Z DTEND:20200515T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/6 DESCRIPTION:Title: The number of closed ideals in $L(L_p)$\nby Gideon Schechtman ( Weizmann Institute of Science) as part of Banach spaces webinars\n\n\nAbst ract\nI intend to review what is known about the closed ideals in the Bana ch algebras $L(L_p(0\,1))$. Then concentrate on a recent result of Bill Johnson and myself showing that for $1\\lt p\\not= 2\\lt \\infty$ there are exactly $2^{2^{\\aleph_0} }$ different closed ideals in $L(L_p(0\,1))$.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Martin (University of Granada) DTSTART:20200529T140000Z DTEND:20200529T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/7 DESCRIPTION:Title: On Quasi norm attaining operators between Banach spaces\nby Mig uel Martin (University of Granada) as part of Banach spaces webinars\n\n\n Abstract\nThis talk deals with a very recently introduced weakened notion of norm attainment for bounded linear operators. An operator $T\\colon X \ \longrightarrow Y$ between the Banach spaces $X$ and $Y$ is quasi norm attaining if there is a sequence $(x_n)$ of norm one elements in $X$ s uch that $(Tx_n)$ converges to some $u\\in Y$ with $\\|u\\|=\\|T\\|$. Norm attaining operators in the usual sense (i.e. operators for which there is a point in the unit ball where the norm of its image equals the norm of t he operator) and compact operators satisfy this definition. The main resul t is that strong Radon-Nikodým operators (such as weakly compact operator s can be approximated by quasi norm attaining operators (even by a stronge r version of the definition)\, a result which does not hold for norm attai ning operators. This allows us to give characterizations of the Radon-Niko dým property in term of the denseness of quasi norm attaining operators f or both domain spaces and range spaces\, extending previous results by Bou rgain and Huff. We will also present positive and negative results on the denseness of quasi norm attaining operators\, characterize both finite dim ensionality and reflexivity in terms of quasi norm attaining operators\, d iscuss conditions to obtain that quasi norm attaining operators are actual ly norm attaining\, study the relationship with the norm attainment of the adjoint operator. We will finish the talk discussing some remarks and ope n questions.\n\nThe content of the talk is based on the recent preprint On Quasi norm attaining operators between Banach spaces by Geunsu Choi\, Yun Sung Choi\, Mingu Jung\, and M iguel Martin.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruno Braga (University of Virginia) DTSTART:20200626T140000Z DTEND:20200626T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/8 DESCRIPTION:by Bruno Braga (University of Virginia) as part of Banach spac es webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Pedro Tradacete (Instituto de Ciencias Matemáticas) DTSTART:20200522T140000Z DTEND:20200522T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/9 DESCRIPTION:Title: Free Banach lattices\nby Pedro Tradacete (Instituto de Ciencias Matemáticas) as part of Banach spaces webinars\n\n\nAbstract\nWe will st art recalling the construction of the free Banach lattice \ngenerated by a Banach space. This notion provides a new link betweeen \nBanach space a nd Banach lattice properties. We will show how this can \nbe useful to ta ckle some problems and discuss some open questions. The \nmaterial of the talk is partially based on the following papers:\n\nThe free Banach lattice generated by a Banach space by Antonio Avilés\, José Rodríguez\, Pedro Tradacete\, J. Funct. Anal. 274 (2018)\, no. 10\, 2955-2977\n\nThe free Banach lattices generated by $\\ell_p$ and $c_0$ by Anto nio Avilés\, Pedro Tradacete\, Ignacio Villanueva\, Rev.Mat. Complutense 32 (2019)\, no. 2\, 353-364.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Denny Leung (National University of Singapore) DTSTART:20200605T140000Z DTEND:20200605T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/10 DESCRIPTION:Title: Local convexity in $L^0$\nby Denny Leung (National University of Singapore) as part of Banach spaces webinars\n\n\nAbstract\nLet $(\\Ome ga\,\\Sigma\,\\mathbb P)$ be a nonatomic probability space and let $L^0(\\ Omega\,\\Sigma\,\\mathbb P)$ be the space of all measurable functions on $ (\\Omega\,\\Sigma\,\\mathbb P)$.\nWe present some results characterizing t he convex sets in $L^0$ that are locally convex with respect to the topolo gy of convergence in measure. The work is motivated by results of Kardara s & Zitkovic (PAMS 2013) and Kardaras (JFA 2014) and is relevant to mathem atical economics/finance.\n\nThe talk is based on joint work with Niushan Gao and Foivos Xanthos:\n\nA lo cal Hahn-Banach Theorem and its applications\, Arch. Math.\, 112(2019)\, 5 21-529. \n\n On local conve xity in $L^0$ and switching probability measures. \n LOCATION:https://researchseminars.org/talk/BanachWebinars/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Noé de Rancourt (Kurt Gödel Research Center) DTSTART:20200612T140000Z DTEND:20200612T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/11 DESCRIPTION:Title: Local Banach-space dichotomies\nby Noé de Rancourt (Kurt Göd el Research Center) as part of Banach spaces webinars\n\n\nAbstract\nI wil l present some results of a recent joint preprint with Wilson Cuellar Carr era and Valentin Ferenczi. These results are generalizations of Banach-spa ce dichotomies due to\nGowers and to Ferenczi–Rosendal\; the original di chotomies aimed at building a classification of separable Banach spaces "u p to subspaces". Our generalizations are "local versions" of the original dichotomies\, that is\, we ensure that the outcome space can be taken in a prescribed family of subspaces. One of the most interesting examples of s uch a family is the family of all non-Hilbertian Banach spaces\; hence\, o ur results are a first step towards a classification of non-Hilbertian\, $ \\ell_2$-saturated Banach spaces\, up to subspaces. If time permits\, I wi ll present some applications of our work to a conjecture by Ferenczi and R osendal about the number of subspaces of a separable Banach space.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (UIC and NSF) DTSTART:20200619T140000Z DTEND:20200619T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/12 DESCRIPTION:Title: Two applications of Arens-Eells spaces to geometric group theory a nd abstract harmonic analysis\nby Christian Rosendal (UIC and NSF) as part of Banach spaces webinars\n\n\nAbstract\nArens-Eells spaces (aka Lips chitz free spaces or transportation cost spaces) give rise to interesting examples of Banach spaces and provide analytic techniques within Banach sp ace geometry\, but are also of importance as a tool for analysing objects outside Banach space theory using functional analytical techniques. I will present two such uses. The first is to abstract harmonic analysis where A rens-Eells spaces can be used to provide a very simple conceptual proof of a recent characterisation of amenability of topological groups due to F. M. Schneider and A. Thom. The second application is to the geometric study of topological groups\, namely\, to establish the Gromov correspondence b etween coarse equivalence and topological couplings in the widest possible setting. Time permitting\, we also discuss some application of the harmon ic analytical tools to the non-linear geometry of Banach spaces.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Gilles Lancien (Besançon) DTSTART:20200703T140000Z DTEND:20200703T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/13 DESCRIPTION:Title: Kalton's interlacing graphs and embeddings into dual Banach spaces \nby Gilles Lancien (Besançon) as part of Banach spaces webinars\n\n\ nAbstract\nA fundamental theorem of Aharoni (1974) states that every separ able metric spaces bi-Lipschitz embeds into $c_0$. It is a major open ques tion to know whether any Banach space containing a Lipschitz copy of $c_0$ must contain a subspace linearly isomorphic to $c_0$. In this talk\, we w ill consider similar questions in relation with the weaker notion of coars e embeddings.\n \nIn a paper published in 2007\, a major step was taken by Nigel Kalton\, who showed that a Banach space containing a coarse copy of $c_0$ cannot have all its iterated duals separable (in particular it cann ot be reflexive). However\, it is still unknown whether such a space can b e a separable dual. In this talk\, we will discuss some aspects of this qu estion. Kalton's argument is based on the use of a special family of metri c graphs that we call ``Kalton's interlacing graphs''. We will give result s about dual spaces containing equi-Lipschitz or equi-coarse copies of the se graphs\, in relation with the Szlenk index\, and show their optimality. \n\n\nThis is a joint work with B. de Mendonça Braga\, C. Petitjean and A . Procházka.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Niels Laustsen (Lancaster University) DTSTART:20200710T140000Z DTEND:20200710T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/14 DESCRIPTION:Title: A $C(K)$-space with few operators and few decompositions\nby N iels Laustsen (Lancaster University) as part of Banach spaces webinars\n\n \nAbstract\nI shall report on j oint work with Piotr Koszmider (IMPAN) concerning the closed subspace of $\\ell_\\infty$ generated by $c_0$ and the characteristic functions of elements of an uncountable\, almost disjoint family $A$ of infinite subset s of the natural numbers. This Banach space has the form $C_0(K_A)$ for a locally compact Hausdorff space $K_A$ that is known under many names\, inc luding $\\Psi$-space and Isbell--Mrówka space.\n\nWe construct an uncount able\, almost disjoint family $A$ such that the algebra of all bounded lin ear operators on $C_0(K_A)$ is as small as possible in the precise sense t hat every bounded linear operator on $C_0(K_A)$ is the sum of a scalar mul tiple of the identity and an operator that factors through $c_0$ (which in this case is equivalent to having separable range). This implies that $C_ 0(K_A)$ has the fewest possible decompositions: whenever $C_0(K_A)$ is wri tten as the direct sum of two infinite-dimensional Banach spaces $X$ and $ Y$\, either $X$ is isomorphic to $C_0(K_A)$ and $Y$ to $c_0$\, or vice ver sa. These results improve\nprevious work of Koszmider in which an extra se t-theoretic hypothesis was required.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Javier Alejandro Chávez-Domínguez (University of Oklahoma) DTSTART:20200717T140000Z DTEND:20200717T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/15 DESCRIPTION:Title: Completely coarse maps are real-linear\nby Javier Alejandro Ch ávez-Domínguez (University of Oklahoma) as part of Banach spaces webinar s\n\n\nAbstract\nIn this talk I will present joint work with Bruno M. Brag a\, continuing the study of the nonlinear geometry of operator spaces that was recently started by Braga and Sinclair.\n\nOperator spaces are Banach spaces with an extra “noncommutative” structure. Their theory sometim es resembles very closely the Banach space case\, but other times is very different. Our main result is an instance of the latter: a completely coar se map between operator spaces (that is\, a map such that the sequence of its amplifications is equi-coarse) has to be real-linear.\n\nContinuing th e search for an “appropriate” framework for a theory of the nonlinear geometry of operator spaces\, we introduce a weaker notion of embeddabilit y between them and show that it is strong enough for some applications. Fo r instance\, we show that if an infinite dimensional operator space $X$ em beds in this weaker sense into Pisier's operator Hilbert space OH\, then $ X$ must be completely isomorphic to OH.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Florent Baudier (TAMU) DTSTART:20200724T140000Z DTEND:20200724T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/16 DESCRIPTION:Title: $L_1$-embeddability of lamplighter metrics\nby Florent Baudier (TAMU) as part of Banach spaces webinars\n\n\nAbstract\nLamplighter group s are important and well-studied objects in (geometric) group theory as th ey provide examples of groups with a variety of interesting geometric/alge braic properties. The lamplighter construction can naturally be extended t o apply to graphs and is instrumental in the study of random walks on grap hs. \nHowever\, much remains to be understood regarding the embeddability of lamplighters groups or graphs into classical Banach spaces.\nInspired b y works on the earthmover distance I will explain how the machinery of sto chastic embeddings into tree metrics can be fruitfully applied to the stud y of $L_1$-embeddability of lamplighter metrics and how it provides genera l upper bounds on the $L_1$-distortion of finite lamplighter graphs (and g roups). I will then discuss an application to the coarse embeddability of the planar lamplighter group and if time permits an application to linear embeddings of Arens-Eells spaces over finite metric spaces into finite-dim ensional $\\ell_1$-spaces. The talk will be targeted towards non-specialis ts.\n\nBased on joint works with P. Motakis (UIUC)\, Th. Schlumprecht (Tex as A&M)\, and A. Zsák (Peterhouse\, Cambridge)\n LOCATION:https://researchseminars.org/talk/BanachWebinars/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ferenczi (University of São Paulo) DTSTART:20200731T140000Z DTEND:20200731T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/17 DESCRIPTION:Title: On envelopes and $L_p$ spaces\nby Valentin Ferenczi (Universit y of São Paulo) as part of Banach spaces webinars\n\n\nAbstract\nThis tal k is based on a work in progress with Jordi Lopez-Abad. \n\n\nWe define\, inside a given space $X$\, the envelope ${\\rm Env}(Y)$ of \na subspace $Y $ as the largest subspace such that\, for any net of surjective isometries on $X$\, pointwise convergence to the identity on $Y$ implies pointwise convergence to the identity on ${\\rm Env}(Y)$. This is reminiscent of the study of Korovkin sets in spaces $C(K)$ or $L_p(\\mu)$ (initiated by P.P . Korovkin in 1960).\n\nWe shall mention some results of a\nrecent paper o f J. Lopez-Abad\, B. Mbombo\, and S. Todorcevic and myself (2019): differe nt notions of ultrahomogeneity of Banach spaces will be stated (AUH\, Fra ïssé) which are relevant to multidimensional versions of Mazur rotations problem. Known examples of these are the Gurarij space and the spaces $L_ p$'s for $p \\neq 4\,6\,8\,\\ldots$. We shall address the conjecture that these are the only separable examples.\n\n The notion of envelope is espec ially relevant to the study of AUH or Fraïssé spaces. \nIn particular we shall compute explicitly certain envelopes in $L_p$-spaces and conclude b y giving a meaning to potentially new objects such as $L_p/\\ell_2$\, $L_ p/L_q$\, $L_p/\\ell_q$\, for appropriate values of $p$ and $q$.\n\n\nParti ally supported by Fapesp\, 2016/25574-8 and CNPq\, 303731/2019-2.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Beanland (Washington and Lee) DTSTART:20200403T140000Z DTEND:20200403T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/18 DESCRIPTION:Title: Closed ideals of operators on the Tsirelson and Schreier spaces\nby Kevin Beanland (Washington and Lee) as part of Banach spaces webinar s\n\n\nAbstract\nSignificant progress has been made in our understanding o f\nthe lattice of closed ideals of the Banach algebra $\\mathcal{B}(X)$ of \nbounded operators on a Banach space $X$ over the last decade. I shall\ns urvey some highlights of this development and then focus on the\noutcomes of an ongoing collaboration with Niels Laustsen (Lancaster University\, UK ) \nand Tomasz Kania (Czech Academy of Sciences) in\nwhich we study the cl osed ideals of $\\mathcal{B}(X)$ in the case\nwhere $X$ is either Tsirels on's Banach space or a Schreier space\nof finite order.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Pete Casazza (University of Missouri) DTSTART:20200807T140000Z DTEND:20200807T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/19 DESCRIPTION:Title: Tsirelson space\, explicitly definable Banach space\, implicitly d efinable Banach space\nby Pete Casazza (University of Missouri) as par t of Banach spaces webinars\n\n\nAbstract\nWe prove that Tsirelson's space cannot be defined explicitly from the classical Banach sequence spaces.\n We also prove that any Banach space that is explicitly definable from a cl ass of spaces that contain $\\ell_p$ or $c_0$ must contain $\\ell_p$ or $c _0$ as well.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Young (NYU) DTSTART:20200814T140000Z DTEND:20200814T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/20 DESCRIPTION:Title: Metric differentiation and Lipschitz embeddings in $L_p$ spaces\nby Robert Young (NYU) as part of Banach spaces webinars\n\n\nAbstract\n Kadec and Pełczyński showed that if $1\\le p\\lt 2\\lt q\\lt \\infty$ an d $X$ is a Banach space that embeds into both $L_p$ and $L_q$\, then $X$ i s isomorphic to a Hilbert space. The search for metric analogues of such a result is intertwined with the Ribe program and metric theories of type a nd cotype. Recently\, with Assaf Naor\, we have constructed a metric space based on the Heisenberg group which embeds into $L_1$ and $L_4$ but not i n $L_2$. In this talk\, we will describe this example\, explain why embedd ings of the Heisenberg group into Banach spaces must be "bumpy" at many sc ales\, and discuss how to bound the bumpiness of Lipschitz maps to Banach spaces.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Khazhakanush Navoyan (Thompson Rivers University) DTSTART:20200821T140000Z DTEND:20200821T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/21 DESCRIPTION:Title: The positive Schur property on spaces of regular multilinear opera tors\nby Khazhakanush Navoyan (Thompson Rivers University) as part of Banach spaces webinars\n\n\nAbstract\nIn this paper we give necessary and sufficient conditions for the space of regular multilinear operators from the product of Banach lattices to a Dedekind complete Banach lattice to ha ve the positive Schur property. We also characterize the positive Schur pr operty on the positive projective mm-fold tensor product of Banach lattice s\, $m\\in\\mathbb{N}$\, and on its dual. This is a joint work with Gerald o Botelho\, Qingying Bu and Donghai Ji.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Mary Angelica Gramcko-Tursi (UIUC) DTSTART:20200904T140000Z DTEND:20200904T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/22 DESCRIPTION:Title: A separable universal homogeneous Banach lattice\nby Mary Ange lica Gramcko-Tursi (UIUC) as part of Banach spaces webinars\n\n\nAbstract\ nWe prove the existence of a separable approximately ultra-homogeneous Ban ach lattice BL that is isometrically universal for separable Banach lattic es. This is done by showing that the class of Banach lattices has the Amal gamation Property\, and thus finitely generated Banach lattices form a met ric Fraïssé class. Some additional results about the structural properti es of BL are also proven.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Bence Horváth (Institute of Mathematics of the Czech Academy of S ciences) DTSTART:20200911T140000Z DTEND:20200911T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/23 DESCRIPTION:Title: When are surjective algebra homomorphisms of $\\mathcal{B}(X)$ aut omatically injective?\nby Bence Horváth (Institute of Mathematics of the Czech Academy of Sciences) as part of Banach spaces webinars\n\n\nAbst ract\nA classical result of Eidelheit asserts that if $X$ and $Y$ are Bana ch\nspaces then they are isomorphic if and only if their algebras of\noper ators $\\mathcal{B}(X)$ and $\\mathcal{B}(Y)$ are isomorphic as Banach\nal gebras\, in the sense that there is a continuous bijective algebra\nhomomo rphism $\\psi: \\\, \\mathcal{B}(X) \\rightarrow \\mathcal{B}(Y)$. It is\n natural to ask whether for some class of Banach spaces $X$ this theorem\nc an be strengthened in the following sense: If $Y$ is a non-zero Banach\nsp ace and $\\psi: \\mathcal{B}(X) \\rightarrow \\mathcal{B}(Y)$ is a\nsurjec tive algebra homomorphism\, is $\\psi$ automatically injective?\n\nIt is e asy to see that for a ``very nice'' class Banach spaces\, such as\n$c_0$ a nd $\\ell_p$\, where $1 \\leq p < \\infty$\, the answer is positive.\nFurt her examples include $\\ell_{\\infty}$ and $( \\oplus_{n=1}^{\\infty}\n\\e ll_2^n )_{c_0}$ and its dual space $\\left( \\oplus_{n=1}^{\\infty}\n\\ell _2^n \\right)_{\\ell_1}$\, and the arbitrarily distortable Banach space\n$ \\mathbf{S}$ constructed by Schlumprecht. In recent joint work with\nTomas z Kania it was shown that ``long'' sequence spaces of the form\n$c_0(\\lam bda)$\, $\\ell_{\\infty}^c(\\lambda)$ and $\\ell_p(\\lambda)$ (where\n$1 \ \leq p < \\infty$) also enjoy this property.\n\nIn the other direction\, w ith the aid of a result of\nKania--Koszmider--Laustsen we will show that f or any separable\,\nreflexive Banach space $X$ there is a Banach space $Y_ X$ and a\nsurjective algebra homomorphism $ \\psi: \\\, \\mathcal{B}(Y_X) \\rightarrow\n\\mathcal{B}(X)$ which is not injective.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Tommaso Russo (Czech Technical University in Prague) DTSTART:20200828T140000Z DTEND:20200828T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/24 DESCRIPTION:Title: Asplund Banach spaces with norming Markuševič bases\nby Tom maso Russo (Czech Technical University in Prague) as part of Banach spaces webinars\n\n\nAbstract\nThe first existence result for norming Markuševi č bases (M-bases\, for short) in Banach spaces is perhaps due to Markuše vič\, who proved that every separable Banach space admits a 1-norming M-b asis. After the introduction of projectional resolutions of the identity\, it became clear that such bases also exist in every reflexive Banach spac e.\n\nIn order to understand the strength of the said notion\, a natural p roblem at the time was then to characterise those (non-separable) Banach s paces that admit a norming M-basis. Perhaps the main question\, due origin ally to John and Zizler and that was solved very recently by P. Hájek\, w as whether every weakly compactly generated (WCG) Banach space admits a no rming M-basis.\n\nIn the converse direction\, it was asked by Gilles Godef roy if an Asplund space with a norming M-basis is necessarily WCG. In the talk\, based on a joint work with P. Hájek\, J. Somaglia\, and S. Todorč ević\, we shall discuss our recent negative answer to the latter question . Moreover\, the construction yields an interesting example of a scattered compact space that also solves a question due to Wiesław Kubiś and Arka dy Leiderman.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Phillips (University of Oregon) DTSTART:20200918T140000Z DTEND:20200918T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/25 DESCRIPTION:Title: Operator algebras on $L_p$ spaces\nby Chris Phillips (Universi ty of Oregon) as part of Banach spaces webinars\n\n\nAbstract\nSurprisingl y\, there appears to be a rich theory of "C* like"\noperator algebras on $ L_p$ spaces. It is far from actual C*-algebras\,\nbut analogs of some of t he basic examples of C*-algebras have\nanalogs on $L_p$ spaces which share at least some of the properties\nof the C* examples. Some of the methods of proof are very different.\n\nThere are many open problems. We do not ev en have a definition of\nwhat it means for an $L_p$ operator algebra to be "C* like"--just\nsome heuristic criteria.\n\nThis talk will try to give a n impression of the current state of\nthe theory\, focussing on several cl asses of examples. It will not\nassume significant knowledge of C*-algebra s.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Paata Ivanisvili (North Carolina State) DTSTART:20200925T140000Z DTEND:20200925T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/26 DESCRIPTION:Title: Sharpening the triangle inequality in $L_p$ spaces\nby Paata I vanisvili (North Carolina State) as part of Banach spaces webinars\n\n\nAb stract\nThe classical triangle inequality in $L_p$ estimates the norm of the sum of two functions in terms of the sums of the norms of these functi ons. \nPerhaps one drawback of this estimate is that it does not see how "orthogonal" these functions are. \nFor example\, if $f$ and $g$ are not identically zero and they have disjoint supports then the triangle inequal ity is pretty strict (say for $p>1$). \nMotivated by the $L_2$ case\, wher e one has a trivial inequality $||f+g||^2 \\leq ||f||^2 + ||g||^2 + 2 |f g|_1$\, one can think about the quantity $|fg|_1$ as measuring the "overl ap" between $f$ and $g$. \nWhat is the correct analog of this estimate i n $L_p$ for $p$ different than 2? My talk will be based on a joint work wi th Carlen\, Frank and Lieb where we obtain one extension of this estimate in $L_p$\, thereby proving and improving the suggested possible estimates by Carbery\, and another work with Mooney where we further refine these e stimates. The estimates will be provided for all real $p$'s.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pelczar-Barwacz (Jagiellonian University) DTSTART:20201002T140000Z DTEND:20201002T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/27 DESCRIPTION:Title: Small operator ideals on the Schlumprecht and Schreier spaces\ nby Anna Pelczar-Barwacz (Jagiellonian University) as part of Banach space s webinars\n\n\nAbstract\nI report on the joint work with Antonis Manoussa kis\, showing that there are $2^{2^{\\aleph_0}}$ many different closed ope rator ideals on the Schlumprecht space and every Schreier space of finite order admits a chain of the cardinality $2^{\\aleph_0}$ of closed operator ideals.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Temlyakov (University of South Carolina) DTSTART:20201009T140000Z DTEND:20201009T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/28 DESCRIPTION:Title: Sampling discretization of integral norms\nby Vladimir Temlyak ov (University of South Carolina) as part of Banach spaces webinars\n\n\nA bstract\nThe talk is devoted to discretization of integral norms of functi ons from\na given finite dimensional subspace. Even though this problem is extremely important in applications\, its systematic study has begun rece ntly.\nIn this talk we discuss a conditional theorem for all integral norm s $L_q$\, $1\\le q<\\infty$.\nA new technique\, which works well for disc retization of the integral norms\, was used. It is\na combination of proba bilistic technique with results on the entropy numbers in the uniform norm .\nWe discuss the behavior of the entropy numbers of classes of functions with bounded integral norms from a given finite dimensional linear subspa ce. \nUpper bounds of these entropy numbers in the uniform norm are ob tained and applied \nto establish a Marcinkiewicz type discretization theorem for integral norms of functions from a given finite dimensio nal subspace. \nAs an application of the general conditiona l theorem\, we discuss a new Marcinkiewicz type\ndiscretization for the m ultivariate trigonometric polynomials with frequencies from the hyperbolic crosses.\nIt is shown that recently developed techniques allow us to impr ove the known results in this direction.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/28/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitchell Taylor (UC Berkeley) DTSTART:20201016T140000Z DTEND:20201016T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/29 DESCRIPTION:Title: Free Banach lattices: subspace structure and basic sequences\n by Mitchell Taylor (UC Berkeley) as part of Banach spaces webinars\n\n\nAb stract\nGiven a Banach space E\, one can associate a Banach lattice FBL[E] with the property that every bounded operator from E to a Banach lattice X extends uniquely to a lattice homomorphism from FBL[E] into X. We will d iscuss the structure of FBL[E]\, and give complete answers to questions li ke when does an embedding of E into F induce a lattice embedding of FBL[E] into FBL[F]? This is joint work with Timur Oikhberg\, Pedro Tradacete and Vladimir Troitsky.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Przemysław Wojtaszczyk (Polish Academy of Sciences) DTSTART:20201023T140000Z DTEND:20201023T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/30 DESCRIPTION:Title: Quasi-greedy bases in $p$-Banach spaces\nby Przemysław Wojtas zczyk (Polish Academy of Sciences) as part of Banach spaces webinars\n\n\n Abstract\nThis talk is based on the paper F. Albiac\, J.L. Ansorena and P. W. \nOn certain subspaces of $\\ell_p$ for $0\\lt p\\le 1$ and \ntheir app lications to conditional quasi-greedy bases in $p$-Banach spaces\, Mathem atische Annalen--available on line.\n \nWe construct new quasi-greedy base s in $\\ell_p$ and in the \nkernels of certain quotient maps from $\\ell_p $ onto $L_p$\,\n$0\\lt p\\leq 1$ and study its properties. We note that all the kernels we study are isomorphic\; we denote this space as ${\\mat hfrak l}_p$. \nWe show that there is continuum of non-equivalent quasi-gr eedy\nbases in $\\ell_p$ and ${\\mathfrak l }_p$ and we study the\n cond itionality of those bases.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Victor Reis (University of Washington) DTSTART:20201030T140000Z DTEND:20201030T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/31 DESCRIPTION:Title: An Elementary Exposition of Pisier's Inequality\nby Victor Rei s (University of Washington) as part of Banach spaces webinars\n\n\nAbstra ct\nPisier's inequality is central in the study of normed spaces and has i mportant applications in geometry. We provide an elementary proof of this inequality by constructing an explicit linear proxy function for a suitabl e probability distribution\, thus avoiding some non-constructive steps in previous proofs. We also show a simplification of Bourgain's construction which is sufficient to give a nearly tight matching lower bound.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Dirk Werner (Freie Universität Berlin) DTSTART:20201106T150000Z DTEND:20201106T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/32 DESCRIPTION:Title: Vector space structure in the set of norm attaining functionals\nby Dirk Werner (Freie Universität Berlin) as part of Banach spaces web inars\n\n\nAbstract\nThe talk discusses the existence (or non-existence) o f vector subspaces of\nthe dual space consisting entirely of norm attainin g functionals.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Eva Pernecka (Czech Technical University in Prague) DTSTART:20201113T150000Z DTEND:20201113T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/33 DESCRIPTION:Title: Lipschitz free spaces and their biduals\nby Eva Pernecka (Czec h Technical University in Prague) as part of Banach spaces webinars\n\n\nA bstract\nWe will study continuous linear functionals on Lipschitz spaces w ith special focus on those belonging to canonical preduals\, the Lipschitz free spaces. We will show that in order to verify weak$^*$ continuity of a functional\, it suffices to do so for bounded monotone nets of Lipschitz functions. Then\, after introducing a notion of support for the functiona ls\, we will discuss their relation to measures. In particular\, we will i dentify the functionals induced by measures as those functionals that admi t a Jordan-like decomposition into a positive and a negative part. The tal k will be based on joint work with Ramón J. Aliaga.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Jamal Kawach (University of Toronto) DTSTART:20201120T150000Z DTEND:20201120T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/34 DESCRIPTION:Title: Approximate Ramsey properties of Fréchet spaces\nby Jamal Kaw ach (University of Toronto) as part of Banach spaces webinars\n\n\nAbstrac t\nIn this talk we will consider various Fraïssé-theoretic aspects of Fr échet spaces\, which we view as topological vector spaces equipped with a compatible sequence of semi-norms. We will show that certain classes of f inite-dimensional Fréchet spaces satisfy a version of the approximate Ram sey property for Banach spaces. We will then see how this property is rela ted to the topological dynamics of the isometry groups of approximately ul trahomogeneous Fréchet spaces. This talk contains joint work in progress with Jordi López-Abad.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonis Manoussakis (Technical University of Crete) DTSTART:20201127T150000Z DTEND:20201127T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/35 DESCRIPTION:Title: A variant of the James tree space\nby Antonis Manoussakis (Te chnical University of Crete) as part of Banach spaces webinars\n\n\nAbstra ct\nWe will discuss the first part of a work in progress\, leading to the construction of an\n $\\ell_{2}$-saturated $d_{2}-$H.I. space. The class of\n $d_{2}$-H.I. Banach spaces is defined in a recent work of W.Cuella r\n Carrera\, N. de Rancourt and V. Ferenczi where also the problem of\n the existence of $\\ell_{2}$-saturated $d_{2}$-H.I space was posed. In\n this talk we will present a classical analogue of this space\, which\n is a reflexive space with an unconditional basis\, based on the James tre e construction. We will discuss its properties and its connection to the desired $d_{2}$-H.I space.\n\nJoint work with Spiros Argyros and Pavlos M otakis\n LOCATION:https://researchseminars.org/talk/BanachWebinars/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Schlumprecht (Texas A&M) DTSTART:20201204T150000Z DTEND:20201204T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/36 DESCRIPTION:by Thomas Schlumprecht (Texas A&M) as part of Banach spaces we binars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Jose Luis Ansorena (Jose Luis Universidad de La Rioja) DTSTART:20201211T150000Z DTEND:20201211T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/37 DESCRIPTION:by Jose Luis Ansorena (Jose Luis Universidad de La Rioja) as p art of Banach spaces webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Keith Ball (University of Warwick) DTSTART:20201215T163000Z DTEND:20201215T173000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/38 DESCRIPTION:Title: Restricted Invertibility\nby Keith Ball (University of Warwick ) as part of Banach spaces webinars\n\n\nAbstract\nI will briefly discuss the Kadison-Singer problem and then explain a beautiful argument of Bourga in and Tzafriri that I will include in a forthcoming article in a volume d edicated to Jean Bourgain.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Bill Johnson (Texas A&M) DTSTART:20210108T150000Z DTEND:20210108T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/39 DESCRIPTION:Title: Homomorphisms from $L(\\ell_p)$ and $L(L_p)$\nby Bill Johnson (Texas A&M) as part of Banach spaces webinars\n\n\nAbstract\nThis is joint work with N. C. Phillips and G.\nSchechtman.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Lechner (Johannes Kepler Universität Linz) DTSTART:20210115T150000Z DTEND:20210115T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/40 DESCRIPTION:Title: Restriced invertibility\, subsymmetric bases and factorization \nby Richard Lechner (Johannes Kepler Universität Linz) as part of Banach spaces webinars\n\n\nAbstract\nGiven an unconditional normalized basis $( e_j)_{j=1}^n$ of a Banach space $X_n$\, we consider\nconditions under whic h an operator $T\\colon X_n\\to X_n$ with ``large diagonal'' can be invert ed when\nrestricted to $X_\\sigma = [e_j : j\\in\\sigma]$ for a ``large'' set $\\sigma\\subset \\{1\,\\ldots\,n\\}$\n(restricted invertibility). We then discuss restricted invertibility and its close connection to\nfinite dimensional quantitative factorization.\n\nIn the second part of the talk \, we show that subsymmetric Schauder bases $(e_j)$ of an infinite\ndimens ional Banach space $X$ have the factorization property\, i.e.\\@ the ident ity $I_X$ on $X$\nfactors through every bounded operator $T\\colon X\\to X $ with large diagonal. In Banach spaces with a\nSchauder basis\, this type of result can often be proved using gliding-hump techniques\, but in\nnon -separable Banach spaces gliding-hump techniques seem unfeasible. However \, if $(e_j^*)$ is a\nnon-$\\ell^1$-splicing (there is no disjointly suppo rted $\\ell^1$-sequence in $X$) subsymmetric\nweak$^*$ Schauder basis for the dual $X^*$ of $X$\, $(e_j^*)$ also has the factorization property.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramon Aliaga (Universitat Politècnica de València) DTSTART:20210122T150000Z DTEND:20210122T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/41 DESCRIPTION:Title: The Radon-Nikodým and Schur properties in Lipschitz-free spaces\nby Ramon Aliaga (Universitat Politècnica de València) as part of Ban ach spaces webinars\n\n\nAbstract\nIn this talk I will sketch the proof th at\, for \nLipschitz-free spaces $\\mathcal{F}(M)$ over complete metric s paces \n$M$\, several Banach space properties are equivalent including th e \nRadon-Nikodým property\, the Schur property\, the Krein-Milman prope rty\, \nor not containing copies of $L_1$. These properties hold exactly when \n$M$ is a purely 1-unrectifiable metric space. For compact $M$\, th ese \nproperties are also equivalent to $\\mathcal{F}(M)$ being a dual Ba nach \nspace. The talk will be based on joint work with C. Gartland\, C. \nPetitjean and A. Procházka.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavlos Motakis (York University) DTSTART:20210129T150000Z DTEND:20210129T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/42 DESCRIPTION:Title: The space $L_1(L_p)$ is primary\nby Pavlos Motakis (York Unive rsity) as part of Banach spaces webinars\n\n\nAbstract\nWe show that $L_1( L_p)$\, the space of Bochner integrable functions with values in $L_p$\, $ 1\\lt p\\lt\\infty$\, is primary\, meaning that\, whenever we represent $ L_1(L_p)$ as a complemented sum of two spaces one of them has to be isomor phic to $L_1(L_p)$. More generally\, the same result can be shown for $L _1(X)$\, where $X$ is closed linear span of the Haar system in a rearran gement invariant Banach space over $[0\,1)$\, except $L_\\infty$.\n\nThis is joint work with R. Lechner\, P.F.X Müller\, and Th. Schlumprecht.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Sophie Grivaux (Université de Lille) DTSTART:20210219T150000Z DTEND:20210219T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/43 DESCRIPTION:Title: Typical properties of contractions on $\\ell_p$-spaces\nby Sop hie Grivaux (Université de Lille) as part of Banach spaces webinars\n\n\n Abstract\nGiven a separable Banach space $X$ of infinite dimension\, one c an consider\non the space $\\mathcal{B}(X)$ of bounded linear operators on $X$ several\nnatural topologies which turn the closed unit ball\n$B_1(X)= \\{T\\in\\mathcal{B}(X)\;||T||\\le 1\\}$ into a Polish space\, i.e. a\nsep arable and completely metrizable space.\n\nIn these talk\, I will present some results concerning typical properties\nin the Baire Category sense of operators of $B_1(X)$ for these\ntopologies when $X$ is a $\\ell_p$-space \, our main interest being to\ndetermine whether typical contractions on t hese spaces have a non-trivial\ninvariant subspace or not.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Ben Wallis (Elgin Community College) DTSTART:20210226T150000Z DTEND:20210226T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/44 DESCRIPTION:by Ben Wallis (Elgin Community College) as part of Banach spac es webinars\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Antonio Avilés López (Universidad de Murcia) DTSTART:20210305T150000Z DTEND:20210305T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/45 DESCRIPTION:Title: Sequential octahedrality and L-orthogonal elements\nby Antonio Avilés López (Universidad de Murcia) as part of Banach spaces webinars\ n\n\nAbstract\nGiven a Banach space $X$\, we consider the following two is ometric properties\, variations on the notion of octahedrality that can be traced back to the work of B. Maurey:\n\n1. There is an element $e^{**}$ in the sphere of the bidual such that $\\|e^{**}+x\\| = 1 + \\|x\\|$ for every $x\\in X$.\n\n2. There is a sequence $(e_n)$ in the sphere of $X$ su ch that $\\lim_n \\|e_n+x\\| = 1 + \\|x\\|$\n\n\nUncountable sums provide examples that 1 does not imply 2. But the converse is unclear. It is natur al to conjecture that a weak$^*$-cluster point of the sequence $(e_n)$ wou ld give the desired $e^{**}$. This turns out to be independent of the usua l axioms of set theory. The proof involves understanding different kinds o f ultrafilters that may or may not exist\, as well as a filter version of the Lebesgue dominated convergence theorem\, similar to those considered b y V. Kadets and A. Leonov. This is a joint work (in progress) with G. Mart \\'{\\i}nez Cervantes and A. Rueda Zoca.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Paul Müller (Johannes Kepler Universität Linz) DTSTART:20210319T140000Z DTEND:20210319T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/46 DESCRIPTION:Title: Complex Convexity Estimates\, Extensions to $R ^n$\, and log-Sobol ev Inequalities.\nby Paul Müller (Johannes Kepler Universität Linz) as part of Banach spaces webinars\n\n\nAbstract\nThe talk is based on join t work with P.Ivanishvili (North\nCarolina State University)\, A. Lindenb erger (JKU) and M.\nSchmuckenschlaeger (JKU).\n\nWe extend complex uniform convexity estimates to $R^n$ and determine\nthe corresponding best cons tants. Furthermore we provide the link to\nlog-Sobolev inequalities on the unit-sphere of $R^n$ and discuss several\nopen conjectures related to our work.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikael de la Salle (ENS Lyon) DTSTART:20210212T150000Z DTEND:20210212T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/47 DESCRIPTION:Title: On a duality between Banach spaces and operators\nby Mikael de la Salle (ENS Lyon) as part of Banach spaces webinars\n\n\nAbstract\nMost classical local properties of a Banach spaces (for example type or cotype \, UMD) are defined in terms of the boundedness of vector-valued operators between Lp spaces or their subspaces. It was in fact proved by Hernandez in the early 1980s that this is the case of any property that is stable by Lp direct sums and finite representability. His result can be seen as one direction of a bipolar theorem for a non-linear duality between Banach sp aces and operators. I will present the other direction and describe the bi polar of any class of operators for this duality. The talk will be based o n my recent preprint.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Johann Langemets (University of Tartu) DTSTART:20210312T150000Z DTEND:20210312T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/48 DESCRIPTION:Title: A characterization of Banach spaces containing $\\ell_1(\\kappa)$ via ball-covering properties\nby Johann Langemets (University of Tartu ) as part of Banach spaces webinars\n\n\nAbstract\nIn 1989\, G. Godefroy p roved that a Banach space contains an isomorphic copy of $\\ell_1$ if and only if it can be equivalently renormed to be octahedral. It is known that octahedral norms can be characterized by means of covering the unit spher e by a finite number of balls. This observation allows us to connect the t heory of octahedral norms with ball-covering properties of Banach spaces i ntroduced by L. Cheng in 2006. Following this idea\, we extend G. Godefroy 's result to higher cardinalities. We prove that\, for an infinite cardina l $\\kappa$\, a Banach space $X$ contains an isomorphic copy of $\\ell_1(\ \kappa^+)$ if and only if it can be equivalently renormed in such a way th at its unit sphere cannot be covered by $\\kappa$ many open balls not cont aining $\\alpha B_X$\, where $\\alpha\\in (0\,1)$. We also investigate the relation between ball-coverings of the unit sphere and octahedral norms i n the setting of higher cardinalities. This is a joint work with S. Ciaci and A. Lissitsin.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Yuval Wigderson (Stanford) DTSTART:20210326T140000Z DTEND:20210326T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/49 DESCRIPTION:Title: New perspectives on the uncertainty principle\nby Yuval Wigder son (Stanford) as part of Banach spaces webinars\n\n\nAbstract\nThe phrase ``uncertainty principle'' refers to a wide array of results in several di sparate fields of mathematics\, all of which capture the notion that a fun ction and its Fourier transform cannot both be ``very localized''. The mea sure of localization varies from one uncertainty principle to the next\, a nd well-studied notions include the variance (and higher moments)\, the en tropy\, the support-size\, and the rate of decay at infinity. Similarly\, the proofs of the various uncertainty principles rely on a range of tools\ , from the elementary to the very deep. In this talk\, I'll describe how m any of the uncertainty principles all follow from a single\, simple result \, whose proof uses only a basic property of the Fourier transform: that i t and its inverse are bounded as operators $L^1 \\to L^\\infty$. Using thi s result\, one can also prove new variants of the uncertainty principle\, which apply to new measures of localization and to operators other than th e Fourier transform. This is joint work with Avi Wigderson.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentin Ferenczi (Universidade de São Paulo) DTSTART:20210409T140000Z DTEND:20210409T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/50 DESCRIPTION:Title: There is no largest proper operator ideal\nby Valentin Ferencz i (Universidade de São Paulo) as part of Banach spaces webinars\n\n\nAbst ract\nAn operator ideal $U$ (in the sense of Pietsch) is proper if\n$Spac e(U)$\, the class of spaces $X$ for which $Id_X \\in U$\, is reduced to th e class of finiite-dimensional spaces. Equivalently\, $U$ is proper if $U( X)$ is a proper ideal of $L(X)$ whenever $X$ is infinite dimensional (wher e $U(X)$ denotes the set of operators on $X$ which belong to $U$).\n \nWe answer a question posed by Pietsch in 1979 by proving that there is no la rgest proper operator ideal. Our proof is based on an extension of the co nstruction by Aiena-Gonz\\'alez (2000)\, of an improjective but essentia l operator on Gowers-Maurey's shift space (1997)\, through a new analysis of the algebra of operators on powers of the shift space.\n \nSupported by FAPESP\, project 2016/25574-8\, and CNPq\, grant 303731/2019-2\n LOCATION:https://researchseminars.org/talk/BanachWebinars/50/ END:VEVENT BEGIN:VEVENT SUMMARY:March Boedihardjo (UCLA) DTSTART:20210423T140000Z DTEND:20210423T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/51 DESCRIPTION:Title: Spectral norms of Gaussian matrices with correlated entries\nb y March Boedihardjo (UCLA) as part of Banach spaces webinars\n\n\nAbstract \nAbstract: We give a non-asymptotic bound on the spectral norm of a $d×d $\nmatrix $X$ with centered jointly Gaussian entries in terms of the\ncova riance matrix of the entries. In some cases\, this estimate is sharp\nand removes the $\\sqrt{log d}$ factor in the noncommutative Khintchine\ninequ ality. Joint work with Afonso Bandeira.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Beata Randrianantoanina (Miami University in Ohio) DTSTART:20210430T140000Z DTEND:20210430T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/52 DESCRIPTION:Title: On $L_1$-embeddability of unions of $L_1$-embeddable metric spaces and of twisted unions of hypercubes\nby Beata Randrianantoanina (Miam i University in Ohio) as part of Banach spaces webinars\n\n\nAbstract\nLet $\\mathcal{E}$ be a class of metric spaces\, $(X\,d)$ be a metric space\, and $A\,B$ be metric subspaces of $X$ such that $X=A\\cup B$ and $(A\,d)\ , (B\,d)$ embed bilipschitzly into spaces $E_A\,E_B\\in \\mathcal{E}$ with distortions $D_A\, D_B$\, respectively. Does this imply that there exists a constant $D$ depending only on $D_A\, D_B$\, and the class $\\mathcal{E }$\, so that $(X\,d)$ embeds bilipschitzly into some space $E_X\\in \\math cal{E}$ with distortion $D$?\n \nThis question was answered affirmatively for the class $\\mathcal{E}$ of all ultrametric spaces by Mendel and Naor in 2013\, and for the class $\\mathcal{E}$ of all Hilbert spaces by K. Mak arychev and Y. Makarychev in 2016. K. Makarychev and Y. Makarychev in 2016 conjectured that the answer is negative when $\\mathcal{E}$ is a class of $\\ell_p$-spaces for any fixed $p\\notin\\{2\,\\infty\\}\,$ in particular for $p=1$. In this connection\, Naor in 2015 and Naor and Rabani in 2017 asked whether the metric space known as ``twisted union of hypercubes''\, first introduced by Lindenstrauss in 1964\, and also considered by Johnson and Lindenstrauss in 1986\, embeds into $\\ell_1$.\n \n \nIn this talk I will show how to embed general classes of twisted unions of $L_1$-embeddab le metric spaces into $\\ell_1$\, including twisted unions of hypercubes w hose metrics are determined by concave functions of the $\\ell_1$-norm\, a nd discuss some related results (joint work with Mikhail I. Ostrovskii).\n LOCATION:https://researchseminars.org/talk/BanachWebinars/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Jordi López Abad (UNED) DTSTART:20210507T140000Z DTEND:20210507T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/53 DESCRIPTION:Title: A note on Pelczynski's universal basis space\nby Jordi López Abad (UNED) as part of Banach spaces webinars\n\n\nAbstract\nWe prove that the isometry group of a renorming of the Pelczynski's universal basis spa ce is extremely amenable. To do this\, we see that the class of finite dim ensional normed spaces is a complemented Fraïssé class with the approxim ate Ramsey property. This is a joint work with Jamal Kawach.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Marek Cúth (Charles University in Prague) DTSTART:20210514T140000Z DTEND:20210514T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/54 DESCRIPTION:Title: Lipschitz-free $p$-spaces\nby Marek Cúth (Charles University in Prague) as part of Banach spaces webinars\n\n\nAbstract\nAbstract: In a joint project with F. Albiac\, J. L. Ansorena and M. Doucha we have been recently investigating the class of Lipschitz-free p-Banach spaces\, which is a generalization of the concept of the nowadays quite attractive class of Lipschitz-free spaces (which is covered by the case of $p=1$). In orde r to obtain reasonable generalizations from the case of $p=1$ to the case of $0\\lt p\\le 1$\, we had to develop new techniques which were leading a lso to new results for the classical case of $p=1$. In the talk I would li ke to survey our results from 5 papers which we produced during last 2 yea rs.\n\nA special emphasis will be given to the result contained in our las t paper where we prove that for any metric space $M$ there exists a bounde d metric space $B(M)$ which is topologically homeomorphic to $M$ such that Lipschitz-free $p$-spaces over $M$ and $B(M)$ are linearly isomorphic for every $0\\lt p\\le 1$. This particular result is new even for the classic al case of $p=1$ and as a consequence it provides us a very natural multip lication on the space of Lipschitz functions over any metric space (even u nbounded one) such that this space becomes a Banach algebra.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Hugh Wark (York\, England) DTSTART:20210521T140000Z DTEND:20210521T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/55 DESCRIPTION:Title: Equilateral sets in large Banach spaces\nby Hugh Wark (York\, England) as part of Banach spaces webinars\n\n\nAbstract\nA subset of a Ba nach space is called equilateral if the distances between any two of its d istinct points are the same. In this talk it will be shown that there exis t non separable Banach spaces with no uncountable equilateral sets and ind eed non separable Banach spaces with no infinite equilateral sets.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Harrison H. Gaebler (University of Kansas) DTSTART:20210528T140000Z DTEND:20210528T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/56 DESCRIPTION:Title: Asymptotic Geometry of Banach Spaces that have a Well-Behaved Riem ann Integral\nby Harrison H. Gaebler (University of Kansas) as part of Banach spaces webinars\n\n\nAbstract\nBanach spaces for which Riemann int egrability implies Lebesgue almost everywhere continuity are said to have the Property of Lebesgue\, or to be ``PL-spaces." It is an open problem to derive a full characterization of PL-spaces. In this talk\, I will first give a brief overview of Riemann and Darboux integrability for Banach-valu ed functions\, and I will then introduce the Property of Lebesgue with som e relevant examples. I will next show how the Property of Lebesgue is conn ected to the asymptotic geometry (both global and local) of the underlying Banach space\, and I will present three new results in this direction tha t are to appear later this year in Real Analysis Exchange. Finally\, I wil l discuss two possibilities for future research on characterizing PL-space s\, and a connection between the Property of Lebesgue and the distortion o f the unit sphere as well.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Yoël Perreau (Besançon) DTSTART:20210625T140000Z DTEND:20210625T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/57 DESCRIPTION:by Yoël Perreau (Besançon) as part of Banach spaces webinars \n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Henrik Johannes Wirzenius (University of Helsinki) DTSTART:20210702T140000Z DTEND:20210702T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/58 DESCRIPTION:Title: Closed ideals in the algebra of compact-by-approximable operators< /a>\nby Henrik Johannes Wirzenius (University of Helsinki) as part of Bana ch spaces webinars\n\n\nAbstract\nIn this talk I will present various exam ples of non-trivial closed ideals of the compact-by-approximable quotient algebra $\\mathfrak A_X=\\mathcal K(X)/\\mathcal A(X)$ on Banach spaces $X $ failing the approximation property. Here $\\mathcal K(X)$ denotes the al gebra of compact operators $X\\to X$ and $\\mathcal A(X)=\\overline{\\math cal F(X)}$ is the uniform norm closure of the bounded finite rank operator s $\\mathcal F(X)$.\n\nThe examples include:\n\n(i) If $X$ has cotype 2\, $Y$ has type 2\, $\\mathfrak A_X\\neq\\{0\\}$ and $\\mathfrak A_Y\\neq\\{0 \\}$\, then $\\mathfrak A_{X\\oplus Y}$ has at least 2 (and in some cases up to 8) closed ideals. \n\n(ii) For all $4\\lt p\\lt \\infty$ there are closed subspaces $X\\subset\\ell^p$ and $X\\subset c_0$ such that $\\mathf rak A_X$ has a non-trivial closed ideal.\n\n(iii) A Banach space $Z$ such that $\\mathfrak A_Z$ contains an uncountable lattice of closed ideals.\n\ nThe talk is based on a recent preprint [arXiv:2105.08403] together with H ans-Olav Tylli (University of Helsinki).\n LOCATION:https://researchseminars.org/talk/BanachWebinars/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Nick Lindemulder and Emiel Lorist (Karlsruhe Institute of Technolo gy and University of Helsinki) DTSTART:20210618T140000Z DTEND:20210618T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/59 DESCRIPTION:Title: A discrete framework for interpolation of Banach spaces\nby Ni ck Lindemulder and Emiel Lorist (Karlsruhe Institute of Technology and Uni versity of Helsinki) as part of Banach spaces webinars\n\n\nAbstract\nWe d evelop a discrete framework for the interpolation of Banach spaces\, which contains e.g. the well-known real and complex interpolation methods\, but also more exotic methods like the $\\pm$-method\, the Radamacher interpol ation method and the $\\ell^p$-interpolation method\, as concrete examples . Our method is based on a sequential structure imposed on a Banach space and has both a formulation modelled after the real and the complex interpo lation methods.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Rubén Medina (University of Granada) DTSTART:20210716T140000Z DTEND:20210716T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/60 DESCRIPTION:Title: Compact retractions and the $\\pi$-property of Banach spaces\ nby Rubén Medina (University of Granada) as part of Banach spaces webinar s\n\n\nAbstract\nIn the talk we will focus on Lipschitz retractions of a s eparable \nBanach space $X$ onto its closed and convex generating subsets $K$\, a \nquestion asked by Godefroy and Ozawa in 2014. Our results are co ncerning \nthe case when $K$ is in some quantitative sense small\, namely when $K$ \nis in very little neibourhoods of certain finite dimensional se ctions of \nit. Under such assumptions we obtain a near characterization o f the \n$\\pi$-property (resp. Finite Dimensional Decomposition property) of a \nseparable Banach space $X$. In one direction\, if $X$ admits the Fi nite \nDimensional Decomposition (which is isomorphically equivalent to th e \nmetric-$\\pi$-property) then we will see how to construct a Lipschitz \nretraction onto a (small) generating convex compact $K$. On the other \n hand\, we will prove that if $X$ admits a small (in a precise sense) \ngen erating compact Lipschitz retract then $X$ has the $\\pi$-property. It \ns eems to be an open problem whether the $\\pi$-property is isomorphically \ nequivalent to the metric-$\\pi$-property (a positive answer would turn \n our results into a complete characterization). In the case of dual \nBanac h spaces\, this characterization is indeed valid.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Berasategui (University of Buenos Aires) DTSTART:20210709T140000Z DTEND:20210709T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/61 DESCRIPTION:Title: Bidemocratic bases and their connections with other greedy-type ba ses\nby Miguel Berasategui (University of Buenos Aires) as part of Ban ach spaces webinars\n\n\nAbstract\nIn this talk we will focus on bidemocra tic bases of Banach and quasi-Banach spaces\, and their greedy-like proper ties. In particular\, we will address the relation between bidemocratic ba ses and quasi-greedy bases. On the one hand\, there are subspaces of $\\el l_p$ with bidemocratic bases that are not quasi-greedy. On the other hand\ , for every arbitrary fundamental function $\\varphi$\, there is a Banach space with a bidemocratic\, quasi-greedy conditional Schauder basis whose fundamental funcion grows as $\\varphi$.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Pavlos Motakis (York University) DTSTART:20211015T140000Z DTEND:20211015T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/62 DESCRIPTION:Title: Separable spaces of continuous functions as Calkin algebras\nb y Pavlos Motakis (York University) as part of Banach spaces webinars\n\n\n Abstract\nThe Calkin algebra $\\mathcal{C}al(X)$ of a Banach space $X$ is the quotient algebra of all bounded linear operators $\\mathcal{L}(X)$ on $X$ over the ideal of all compact ones $\\mathcal{K}(X)$. A question that has gathered attention in recent years is what unital Banach algebras admi t representations as Calkin algebras. There is a strong connection between quotients algebras of $\\mathcal{L}(X)$ and the tight control of the oper ators on $X$ modulo a small ideal. We discuss a new contribution to this t opic\, namely that for every compact metric space $K$ there exists a Banac h space $X$ so that $\\mathcal{C}al(X)$ coincides isometrically with $C(K) $ as a Banach algebra.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Abraham Rueda Zoca (Universidad de Murcia) DTSTART:20211105T140000Z DTEND:20211105T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/63 DESCRIPTION:Title: $L$-orthogonal elements and spaces of operators\nby Abraham Ru eda Zoca (Universidad de Murcia) as part of Banach spaces webinars\n\n\nAb stract\nGiven a Banach space $X$\, we say that an element $u\\in X^{**}$ i s $L$-orthogonal if\, for every $x\\in X$\, it follows that\n$$\\Vert x+u\ \Vert=\\Vert x\\Vert+\\Vert u\\Vert.$$\nIn 1989\, G. Godefroy proved that a Banach space $X$ admits an equivalent renorming with non-zero $L$-orthog onal elements if\, and only if\, $X$ contains an isomorphic copy of $\\ell _1$. Moreover\, G. Godefroy and N. J. Kalton proved (in 1989 too) that a s eparable space $X$ has non-zero $L$-orthogonal elements if\, and only if\, the following condition holds:\n\\begin{center}\nFor every finite-dimensi onal subspace $F$ of $X$ and every $\\varepsilon>0$ there exists $x\\in S_ X$ so that $\\Vert y+\\lambda x\\Vert\\geq (1-\\varepsilon)(\\Vert y\\Vert +\\vert\\lambda\\vert)$ holds for every $y\\in F$ and every $\\lambda\\in\ \mathbb R$.\n\\end{center}\n\nIn this talk we will examine the validity of this theorem for non-separable Banach spaces. For this\, and for other re sults of the structure of the set of $L$-orthogonal elements\, the Banach spaces of linear bounded operators between two Banach spaces will play a c rucial role.\n\n\n\nThe author was supported by Juan de la Cierva-Formaci\ \'on fellowship FJC2019-039973\, by MTM2017-86182-P (Government of Spain\, AEI/FEDER\, EU)\, by MICINN (Spain) Grant PGC2018-093794-B-I00 (MCIU\, AE I\, FEDER\, UE)\, by Fundaci\\'on S\\'eneca\, ACyT Regi\\'on de Murcia gra nt 20797/PI/18\, by Junta de Andaluc\\'ia Grant A-FQM-484-UGR18 and by Jun ta de Andaluc\\'ia Grant FQM-0185.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Florent Baudier (Texas A&M) DTSTART:20211112T150000Z DTEND:20211112T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/64 DESCRIPTION:Title: Umbel convexity and the geometry of trees\nby Florent Baudier (Texas A&M) as part of Banach spaces webinars\n\n\nAbstract\nMarkov convex ity is a powerful invariant\, introduced by Lee\, Naor and Peres more than 15 years ago\, which is related to the geometry of (locally finite) trees and (quantitative) uniformly convex renormings.\nIn a joint work with Chr is Gartland we introduced new metric invariants capturing the geometry of countably branching trees. Our main invariant\, called umbel convexity\, w as inspired by Markov convexity and shares many of its desirable features. Most notably\, it provides lower bounds on the distortion/compression req uired when embedding countably branching trees\, and it is stable under ce rtain nonlinear quotients. I will explain the close relationship between u mbel convexity and Rolewicz's property $\\beta$ renormings. If time permit s\, I will discuss the notion of umbel cotype\, a relaxation of umbel conv exity\, and its relevance to the geometry of Heisenberg groups.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Krzsystof Swiecicki (Texas A&M) DTSTART:20211119T150000Z DTEND:20211119T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/65 DESCRIPTION:Title: No dimension reduction for doubling spaces of $\\ell_q$ for $q>2$. \nby Krzsystof Swiecicki (Texas A&M) as part of Banach spaces webinars \n\n\nAbstract\nWe'll provide a new elementary proof for the impossibility of dimension reduction for doubling subsets of $\\ell_q$ for $q>2$. This is done by constructing a family of diamond graph-like objects based on th e construction by Bartal\, Gottlieb\, and Neiman. We'll compare our approa ch with previous results and discuss their advantages and disadvantages. O ne noteworthy consequence of our proof is that it can be naturally general ized to obtain embeddability obstructions into non-positively curved space s or asymptotically uniformly convex Banach spaces. Based on the work with Florent Baudierabd Andrew Swift.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Wyczesany (Tel Aviv) DTSTART:20211203T150000Z DTEND:20211203T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/66 DESCRIPTION:Title: On almost Euclidean and well-complemented subspaces of finite-dime nsional normed spaces\nby Kasia Wyczesany (Tel Aviv) as part of Banach spaces webinars\n\n\nAbstract\nIn this talk I will discuss a version of a n old question of Vitali Milman about almost Euclidean and well-complement ed subspaces. In particular\, I will introduce a notion of ' ε-good point s '\, which allows for a convenient reformulation of the problem. Let (X\, ||·||X) be a normed space. It turns out that if a linear subspace Y ⊂ X consists entirely of ε-good points then the restriction of the norm ||· ||X to Y must be approximately a multiple of the l2 norm and the operator norm of the orthogonal projection onto Y is close to 1. I will present an example of a normed space X of arbitrarily high dimension\, whose Banach-M azur distance from the l2dim X is at most 2\, but such that non of its (ev en two-dimensional) subspaces consists entirely of ε-good points. The tal k is based on joint work with Timothy Gowers.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Chris Gartland (Texas A&M) DTSTART:20211210T150000Z DTEND:20211210T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/67 DESCRIPTION:by Chris Gartland (Texas A&M) as part of Banach spaces webinar s\n\nAbstract: TBA\n LOCATION:https://researchseminars.org/talk/BanachWebinars/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Ostrovskii (St. John's University) DTSTART:20220304T150000Z DTEND:20220304T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/68 DESCRIPTION:Title: Dvoretzky-type theorem for locally finite subsets of a Hilbert spa ce\nby Mikhail Ostrovskii (St. John's University) as part of Banach sp aces webinars\n\n\nAbstract\nThe main result of the talk: Given any $\\va repsilon>0$\, every locally finite subset of $\\ell_2$ admits a $(1+\\vare psilon)$-bilipschitz embedding into an arbitrary infinite-dimensional Bana ch space.\n\n \nThe result is based on two results which are of independen t interest:\n\n \n(1) A direct sum of two finite-dimensional Euclidean spa ces contains a sub-sum of a controlled dimension which is $\\varepsilon$-c lose to a direct sum with respect to a $1$- unconditional basis in a two-d imensional space.\n\n \n(2) For any finite-dimensional Banach space $Y$ an d its direct sum $X$ with itself with respect to a $1$-unconditional basis in a two-dimensional space\, there exists a $(1+\\varepsilon)$-bilipschit z embedding of $Y$ into $X$ which on a small ball coincides with the ident ity map onto the first summand and on a complement of a large ball coincid es with the identity map onto the second summand.\n\n\n(joint with F. Catr ina and S. Ostrovska)\n LOCATION:https://researchseminars.org/talk/BanachWebinars/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Jarosław Swaczyna (Technical University of Łódź) DTSTART:20220422T140000Z DTEND:20220422T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/69 DESCRIPTION:Title: Continuity of coordinate functionals for filter Schauder basis \nby Jarosław Swaczyna (Technical University of Łódź) as part of Banac h spaces webinars\n\n\nAbstract\nGiven a filter of subsets of natural numb ers $F$ we say that a sequence $(x_n)$ is $F$-convergent to $x$ if for eve ry $\\varepsilon>0 $condition $\\{n\\in \n:d(x_n\,x)<\\varepsilon \\}\\in F$ holds. We may use this notion to generalize the idea of Schauder basis\ , namely we say that a sequence $(e_n)$ is an $F$-basis if for every $x\\i n X$ there exists a unique sequence of scalars $(\\alpha_n)$ s.t. $\\sum_{ n\,F} \\alpha_n e_n=x$\, which means that the sequence of partial sums is $F$-convergent to $x$. Once such a notion is introduced it is natural to a sk whenever corresponding coordinate functionals are continuous. Such a qu estion was posed by V. Kadets during the 4th conference Integration\, Vect or Measures\, and Related Topics held in 2011 in Murcia. Surprisingly\, th ere is an obstacle related to the lack of uniform boundedness of functiona ls related to $F$ basis\, due to which we can not find proof of continuity analogous to the classical case. During my talk\, I will discuss the prob lem and provide two proofs of continuity of considered functionals\, which uses under some large cardinal assumptions. This is joint work with Tomas z Kania and Noe de Rancourt\n LOCATION:https://researchseminars.org/talk/BanachWebinars/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Doležal (The Czech Academy of Sciences) DTSTART:20220520T140000Z DTEND:20220520T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/70 DESCRIPTION:Title: Descriptive complexity of Banach spaces\nby Martin Doležal (T he Czech Academy of Sciences) as part of Banach spaces webinars\n\n\nAbstr act\nWe introduce a new natural coding of separable Banach spaces.\nThe se t of codes consists of (pseudo)norms on a certain vector space and is equi pped with a canonical Polish topology.\nWe use this coding to investigate the descriptive complexities of some classical Banach spaces.\nAmong other results\, we show that $\\ell_2$ is\n\n\na) the unique (up to isometry) s eparable Banach space with a closed isometry class\,\n\nb) the unique (up to isomorphism) separable Banach space with an $F_\\sigma$ isomorphism cla ss.\n\n\nThis is a joint work with Marek C\\'uth\, Michal Doucha and Ond\\ v rej Kurka.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Hung Viet Chu (UIUC) DTSTART:20220930T140000Z DTEND:20220930T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/71 DESCRIPTION:Title: A Relaxation of Optimality for the TGA\nby Hung Viet Chu (UIUC ) as part of Banach spaces webinars\n\n\nAbstract\nWe begin by recalling t he Thresholding Greedy Algorithm (TGA) introduced by Konyagin and Temlyako v in 1999. The TGA optimality is described by the notion of greedy and alm ost greedy bases.\nA basis $(e_n)_{n=1}^\\infty$ of a Banach space $X$ (ov er a field $\\mathbb{F}$) is said to be greedy if there exists a constant $\\mathbf C\\geqslant 1$ such that \n\n$$\\|x-G_m(x)\\|\\ \\leqslant\\ \\m athbf C\\inf_{\\substack{|A|\\leqslant m\\\\(a_n)_{n\\in A}\\subset \\math bb{F}}}\\left\\|x-\\sum_{n\\in A}a_ne_n\\right\\|.$$\n\nHere\, $G_m(x)$ is the so-called greedy sum of $x$ of size $m$. The definition of almost gr eedy bases replaces the arbitrary linear combinations on the right by proj ections. \nWe present properties of both greedy and almost bases as well a s their characterizations. \n\nExtending classical results\, we define ($f $\, greedy) bases to satisfy the condition: there exists a constant $\\mat hbf C\\geqslant 1$ such that \n\n$$\\|x-G_m(x)\\|\\ \\leqslant\\ \\mathbf C\\inf_{\\substack{|A|\\leqslant f(m)\\\\(a_n)_{n\\in A}\\subset \\mathbb{ F}}}\\left\\|x-\\sum_{n\\in A}a_ne_n\\right\\|\,$$\n\nwhere $f$ belongs to $\\mathcal{F}$\, a collection that contains functions like $f(x) = cx^{\\ gamma}$ for $c\, \\gamma\\in [0\,1]$. The definition of ($f$\, almost gree dy) is modified accordingly. We give characterizations of these bases\, wh ich help establish the surprising equivalence: if $f$ is a non-identity fu nction in $\\mathcal{F}$\, then a basis is ($f$\, greedy) if and only if i t is ($f$\, almost greedy). We show that ($f$\, greedy) bases form a much wider class as there exist examples of classical bases that are not almost greedy but is ($f$\, greedy) for some $f\\in\\mathcal{F}$.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Freeman (St Louis University) DTSTART:20230210T150000Z DTEND:20230210T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/72 DESCRIPTION:Title: Stable phase retrieval in function spaces\, Part I\nby Daniel Freeman (St Louis University) as part of Banach spaces webinars\n\n\nAbstr act\nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\leq p\\le q \\infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\\geq 1$ such that for any $f \,g\\in E$ we have \n$$\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\||f |-|g|\\|.$$\n In this case\, if $|f|$ is known\, then $f$ is uniquely determined up to an unavoidable global phase factor $\\lambda$\; moreover\ , the phase recovery map is $C$-Lipschitz. Phase retrieval appears in seve ral applied circumstances\, ranging from crystallography to quantum mechan ics.\n\n\nWe will discuss how problems in phase retrieval are naturally re lated to classical notions in the theory of Banach lattices. Through makin g this connection\, we may apply established methods from the subject to a ttack problems in phase retrieval\, and conversely we hope that the ideas and questions in phase retrieval will inspire a new avenue of research in the theory of Banach lattices.\n\nThis talk is based on joint work with Be njamin Pineau\, Timur Oikhberg\, and Mitchell Taylor.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/72/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitchell A. Taylor (UC Berkeley) DTSTART:20230217T150000Z DTEND:20230217T160000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/73 DESCRIPTION:Title: Stable phase retrieval in function spaces\, Part II\nby Mitche ll A. Taylor (UC Berkeley) as part of Banach spaces webinars\n\n\nAbstract \nLet $(\\Omega\,\\Sigma\,\\mu)$ be a measure space\, and $1\\leq p\\leq \ \infty$. A subspace $E\\subseteq L_p(\\mu)$ is said to do stable phase ret rieval (SPR) if there exists a constant $C\\geq 1$ such that for any $f\,g \\in E$ we have \n $$\\inf_{|\\lambda|=1} \\|f-\\lambda g\\|\\leq C\\|| f|-|g|\\|.$$\n In this case\, if $|f|$ is known\, then $f$ is uniquely determined up to an unavoidable global phase factor $\\lambda$\; moreover \, the phase recovery map is $C$-Lipschitz. Phase retrieval appears in sev eral applied circumstances\, ranging from crystallography to quantum mecha nics.\n\n\nIn this talk\, I will present some elementary examples of subsp aces of $L_p(\\mu)$ which do stable phase retrieval\, and discuss the stru cture of this class of subspaces. This is based on a joint work with M. Ch rist and B. Pineau\, as well as a joint work with D. Freeman\, B. Pineau a nd T. Oikhberg.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Kamil Krzysztof Ryduchowski (Warsaw) DTSTART:20230324T140000Z DTEND:20230324T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/74 DESCRIPTION:Title: Equilateral and separated sets in some nonseparable Banach spaces< /a>\nby Kamil Krzysztof Ryduchowski (Warsaw) as part of Banach spaces webi nars\n\n\nAbstract\nA subset $S$ of a Banach space $X$ is called $r$-equil ateral (resp.\, $r$-separated) if any two points of $S$ are in the distanc e exactly $r$ (resp.\, at least $r$) from each other. Whereas Terenzi cons tructed an infinite-dimensional Banach space without infinite equilateral sets\, Elton and Odell proved that the unit sphere of every infinite-dimen sional Banach space contains an infinite $(1+r)$-separated set for some $r >0$. Recently\, some research has been done concerning the uncountable ver sions of these problems\, e.g.\, Kania\, Hajek and Russo proved that the u nit sphere of every nonseparable reflexive Banach spaces contains an uncou ntable $(1+r)$-separated set for some $r>0$. \n\nDuring my talk\, I will p resent some known results concerning this line of research and discuss joi nt results with Piotr Koszmider. In particular\, I will show that\, under some set-theoretic assumptions\, there is an equivalent renorming of the n onseparable Hilbert space $\\ell_2(\\omega_1)$ without uncountable equilat eral sets.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Christian Rosendal (The University of Maryland) DTSTART:20230421T140000Z DTEND:20230421T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/75 DESCRIPTION:Title: On the relation of coarse embeddability between Banach spaces\ nby Christian Rosendal (The University of Maryland) as part of Banach spac es webinars\n\n\nAbstract\nUnder the weak assumption on a Banach space $E$ that $E\\oplus E$ embeds isomorphically into $E$\, we provide a character isation of when a Banach space $X$ coarsely embeds into $E$ via a single n umerical invariant.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Bruce Blackadar (University of Nevada\, Reno) DTSTART:20230512T140000Z DTEND:20230512T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/76 DESCRIPTION:Title: Hilbert Spaces Without Countable AC\nby Bruce Blackadar (Unive rsity of Nevada\, Reno) as part of Banach spaces webinars\n\n\nAbstract\nT his article examines Hilbert spaces constructed from sets whose existence is incompatible with the Countable Axiom of Choice (CC). Our point of view is twofold: (1) We examine what can and cannot be said about Hilbert spac es and operators on them in ZF set theory without any assumptions of Choic e axioms\, even the CC. (2) We view Hilbert spaces as ``quantized'' sets a nd obtain some set-theoretic results from associated Hilbert spaces.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Pelczar-Barwacz (Jagiellonian University) DTSTART:20230505T140000Z DTEND:20230505T150000Z DTSTAMP:20260422T212928Z UID:BanachWebinars/77 DESCRIPTION:Title: A Banach space with an infinite dimensional reflexive quotient ope rator algebra $L(X)/SS(X)$\nby Anna Pelczar-Barwacz (Jagiellonian Univ ersity) as part of Banach spaces webinars\n\n\nAbstract\nI will discuss me thod of constructing a Banach space $X$ such that the algebra of bounded o perators $L(X)$ is a direct sum of an infinite dimensional reflexive Banac h space $V$ and the operator ideal of strictly singular operators $SS(X)$. \nThe space $V$ is spanned by an unconditional basic sequence $(I_s)_{s=0 }^\\infty$ where $I_0$ is the identity on $X$\, whereas each $I_s\, s=1\,2 \,...$ is a projection on some subspace $X_s$ of $X$. The multiplication o n $V$ is defined naturally: $V$ is the unitization of the subalgebra of $L (X)$ spanned by $(I_s)_{s=1}^\\infty$ with the pointwise multiplication.\n LOCATION:https://researchseminars.org/talk/BanachWebinars/77/ END:VEVENT END:VCALENDAR