\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;VALUE=DATE-TIME:20200424T140000Z DTEND;VALUE=DATE-TIME:20200424T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T080801Z 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;VALUE=DATE-TIME:20200501T140000Z DTEND;VALUE=DATE-TIME:20200501T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T080801Z 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;VALUE=DATE-TIME:20200508T140000Z DTEND;VALUE=DATE-TIME:20200508T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T080801Z 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;VALUE=DATE-TIME:20200515T140000Z DTEND;VALUE=DATE-TIME:20200515T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T080801Z 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;VALUE=DATE-TIME:20200529T140000Z DTEND;VALUE=DATE-TIME:20200529T150000Z DTSTAMP;VALUE=DATE-TIME:20231130T080801Z 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