BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Chi-Kwong Li (College of William and Mary\, Virginia)
DTSTART:20200529T150000Z
DTEND:20200529T160000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/1
DESCRIPTION:Title: Quantum states and quantum channels\nby Chi-Kwong Li (College
of William and Mary\, Virginia) as part of Preserver Webinar\n\n\nAbstrac
t\nIn the Hilbert space formulation\, quantum states are density matrices\
, i.e.\, positive semidefinite matrices with trace one\, and quantum chann
els are trace preserving completely positive linear maps on matrices. In t
his talk\, we will present some results on the existence of quantum channe
ls with some special properties. Open problems in constructing special typ
es of quantum channel will be mentioned.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lajos Molnár (University of Szeged)
DTSTART:20200605T110000Z
DTEND:20200605T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/2
DESCRIPTION:Title: Means and their preservers\nby Lajos Molnár (University of S
zeged) as part of Preserver Webinar\n\n\nAbstract\nIn this talk we survey
our recent work on preservers related to operator means.\n\nWe deal with m
orphisms with respect to means as operations on positive definite or semid
efinite cones in operator algebras and consider preservers of norms of mea
ns in similar settings. The first group of questions are motivated by the
study of certain isometries while the second group of problems have a loos
e connection to quantum mechanical symmetry transformations. We discuss po
ssibilities of transforming one mean to another one and\, if time permits\
, we also present some characterizations of specific means.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Peralta (University of Granada)
DTSTART:20200612T150000Z
DTEND:20200612T160000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/3
DESCRIPTION:Title: Tingley's problem for subsets strictly smaller than the unit sphe
re\nby Antonio Peralta (University of Granada) as part of Preserver We
binar\n\n\nAbstract\nThe celebrated Tingley's problem has focused the atte
ntion of a wide community of researchers on preservers in recent years. It
admits the following easy statement: Suppose $\\Delta : S(X) \\to S(Y)$ i
s a surjective isometry between the unit spheres of two Banach spaces $X$
and $Y$. Does $\\Delta$ admit an extension to a surjective linear isometry
from $X$ onto $Y$? This difficult problem remains open even in the case o
f 2-dimensional spaces. A long series of papers has been devoted to provid
e positive answers for some concrete structures\, these partial answers ha
ve produced a wide range of new tools and results with interesting geometr
ic and analytic conclusion.\n\n\nThe reader might guess from the title tha
t we won't limit ourself to Tingley's problem in this talk. It is natural
to challenge the audience to consider other variants. We shall deal with o
ne of the most attractive and we shall consider the posibility of extendin
g surjective isometries between proper subsets of the unit spheres (for ex
ample\, the subset of extreme points of the closed unit ball\, the subset
of positive elements in the unit sphere of $B(H)$\, the subgroup of unitar
y elements in a unital C$^*$-algebra\, the set of unitary elements in a un
ital JB$^*$-algebra\, etcetera). We shall see that negative and positive a
nswers can be obtained.\n\n\n[1] M. Cueto-Avellaneda\, A.M. Peralta\, The
Mazur--Ulam property for commutative von Neumann algebras\, Linear and Mul
tilinear Algebra\, 68\, No. 2\, 337--362 (2020).\n\n \n[2] M. Cueto-Ave
llaneda\, A.M. Peralta\, Can one identify two unital JB$^*$-algebras by th
e metric spaces determined by their sets of unitaries?\, preprint 2020\, a
rXiv:2005.04794\n\n[3] O. Hatori\, L. Molnar\, Isometries of the unitary g
roups and Thompson isometries of the spaces of invertible positive element
s in C*-algebras\, J. Math. Anal. Appl.\, 409\, 158-167 (2014).\n\n[4] G.
Nagy\, Isometries of spaces of normalized positive operators under the ope
rator norm\, Publ. Math. Debrecen\, 92\, no. 1-2\, 243-254 (2018).\n\n[5]
A.M. Peralta\, A survey on Tingley's problem for operator algebras\, Acta
Sci. Math. (Szeged)\, 84\, 81-123 (2018).\n\n[6] A.M. Peralta\, Characteri
zing projections among positive operators in the unit sphere\, Adv. Oper.
Theory\, 3\, no. 3\, 731-744 (2018).\n\n[7] A.M. Peralta\, On the unit sph
ere of positive operators\, Banach J. Math. Anal.\, 13\, no. 1\, 91-112 (2
019).\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matej Bresar (University of Ljubljana and University of Maribor)
DTSTART:20200617T110000Z
DTEND:20200617T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/4
DESCRIPTION:Title: Zero product determined algebras and commutativity preservers
\nby Matej Bresar (University of Ljubljana and University of Maribor) as p
art of Preserver Webinar\n\n\nAbstract\nA (not necessarily associative) al
gebra $A$ over a field $F$ is said to be zero product determined if every
bilinear\nfunctional $f : A \\times A \\to F$ with the property that $ab
= 0$ implies $f(a\, b) = 0$ is of the form $f(a\, b) = \\varphi(ab)$ for
some\nlinear functional $\\varphi$ on $A$.\n\nIn the context of\nBanach a
lgebras\, one adds the assumption that $f$ and $\\varphi$ are continuous.
We will first survey the general theory of zero product determined algebr
as\, and then discuss its applications to commutativity preserving linear
maps.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michiya Mori (University of Tokyo)
DTSTART:20200624T110000Z
DTEND:20200624T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/5
DESCRIPTION:Title: Lattice isomorphisms between projection lattices of von Neumann a
lgebras\nby Michiya Mori (University of Tokyo) as part of Preserver We
binar\n\n\nAbstract\nA von Neumann algebra is a weak operator closed *-sub
algebra of B(H)\,\nwhose study was initiated by Murray and von Neumann in
1930’s. The\ncollection of projections of a von Neumann algebra forms a
lattice\, and\nits geometry has played a very important role in understand
ing the\nstructure of von Neumann algebras for more than 80 years.\n\n\nIn
this talk\, we consider the following fundamental question: What is\nthe
general form of lattice isomorphisms between projection lattices of\nvon N
eumann algebras? Von Neumann gave an answer to this question for\ntype $\\
mathrm{II}_1$ factors. He proved that a lattice isomorphism can be describ
ed\nby means of a ring isomorphism between the algebras of affiliated\nope
rators. However\, apparently no answer to this question has been given\nfo
r the general case (in particular for type $\\mathrm{III}$ von Neumann alg
ebras)\nuntil now. In this talk\, we begin with a brief recap of the class
ical\ntheory of von Neumann algebras\, and then give an answer to our ques
tion\nfor general von Neumann algebras (save type $\\mathrm{I}_1$ and $\\m
athrm{I}_2$) using ring\nisomorphisms between the algebras of locally meas
urable operators. We\nalso consider a better description of ring isomorphi
sms between locally\nmeasurable operator algebras\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Semrl (University of Ljubljana)
DTSTART:20200701T110000Z
DTEND:20200701T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/6
DESCRIPTION:Title: Loewner's theorem for maps on operator domains\nby Peter Semr
l (University of Ljubljana) as part of Preserver Webinar\n\n\nAbstract\nTh
e classical Loewner's theorem states that operator monotone functions on r
eal intervals are described by holomorphic functions on the upper half-pla
ne. We prove an analogue where real intervals are replaced by operator dom
ains\, operator monotone functions by local order isomorphisms\, and upper
half-plane by the set of all bounded operators whose imaginary part is a
positive invertible operator. We will present several results on local ord
er isomorphisms and pay a special attention to the finite-dimensional case
. This is a report on a joint work with Michiya Mori.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bas Lemmens (University of Kent)
DTSTART:20200708T110000Z
DTEND:20200708T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/7
DESCRIPTION:Title: A metric version of a theorem by Poincaré\nby Bas Lemmens (U
niversity of Kent) as part of Preserver Webinar\n\n\nAbstract\nNumerous th
eorems in several complex variables are instances of results in metric geo
metry. In this talk we shall see that a classic theorem due to Poincare\,
which says that there is no biholomorphic map from the polydisc onto the
(open) Euclidean ball in $C^n$ if n is at least $2$\, is a case in point.
In fact\, it is known that exists no surjective Kobayashi distance isomet
ry between these two domains.\n\nIn the talk we shall see how Poincare's t
heorem can be derived from a result for products of proper geodesic metri
c spaces. In fact\, the main goal of the talk is to present a general cri
terion\, in terms of certain asymptotic geometric properties of the indivi
dual metric spaces\, that yields an obstruction for the existence of an is
ometric embedding between product metric spaces.\n\nThe key concepts from
metric geometry involved are: the horofunction boundary of metric spaces\
, the Busemann points\, and the detour distance. These concepts can\, and
have been\, successfully used to analyse preserver problems involving isom
etries.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denny H. Leung (National University of Singapore)
DTSTART:20200715T110000Z
DTEND:20200715T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/8
DESCRIPTION:Title: Nonlinear biseparating maps\nby Denny H. Leung (National Univ
ersity of Singapore) as part of Preserver Webinar\n\n\nAbstract\nLet $X\,Y
$ be topological spaces and $E$\, $F$ be normed spaces. Suppose that $A(X
\,E)$ is a vector subspace of $C(X\,E)$ (space of $E$-valued continuous fu
nctions on $X$) and $A(Y\,F)$ is a subspace of $C(Y\,F)$.\nAn additive map
$T: A(X\,E)\\to A(Y\,F)$ is {\\em disjointness preserving} if \n\\[ \\|f(
x)\\|\\cdot\\|g(x)\\| =0 \\text { for all $x\\in X$ } \\implies \\|Tf(y)\
\|\\cdot\\|Tg(y)\\| =0 \\text { for all $y\\in Y$. }\n\\]\n$T$ is {\\em bi
separating} if it is a bijection and both $T$ and $T^{-1}$ are disjointne
ss preserving.\nIn this talk\, I will propose a definition of ``bisepara
ting'' for general nonlinear mappings. \nThen we will proceed to analyze t
he structure of biseparating maps acting on various types of function spac
es (spaces of continuous functions\, uniformly continuous functions\, Lips
chitz functions\, etc).\n\n\n\n\\bigskip\n\n\n\nPart of the talk is based
on the PhD thesis of Xianzhe Feng\, completed at NUS in 2018.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Javad Mashreghi (Laval University)
DTSTART:20200722T150000Z
DTEND:20200722T160000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/9
DESCRIPTION:Title: On Gleason-Kahane-Zelazko Theorems\nby Javad Mashreghi (Laval
University) as part of Preserver Webinar\n\n\nAbstract\nLet $T: H^p \\to
H^p$ be a linear mapping (no continuity assumption). What can we say about
$T$ if we assume that ``it preserves outer functions''? Another related q
uestion is to consider linear functionals $T: H^p \\to \\mathbb{C}$ (again
\, no continuity assumption) and ask about those functionals whose kernels
do not include any outer function. We study such questions via an abstrac
t result which can be interpreted as the generalized Gleason--Kahane--\\.Z
elazko theorem for modules. In particular\, we see that continuity of endo
morphisms and functionals is a part of the conclusion. We go further and a
lso discuss GKZ in other function spaces\, e.g.\, Bergman\, Dirichlet\, Be
sov\, the little Bloch\, and VMOA and even generally in RKHS.\n\nThis is a
joint work with T. Ransford.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ying-Fen Lin (Queens University Belfast)
DTSTART:20200729T110000Z
DTEND:20200729T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/10
DESCRIPTION:Title: Schur multipliers and positive extensions\nby Ying-Fen Lin (
Queens University Belfast) as part of Preserver Webinar\n\n\nAbstract\nThe
positive completion problem for a partially defined matrix asks when the
unspecified entries can be determined in such a way that the resulting ful
ly defined matrix is positive semi-definite. The problem has attracted a c
onsiderable attention in the literature\, and had been studied using combi
natorial approaches\, until Paulsen\, Power and Smith observed in the late
1980's that it is closely related to completely positive maps and operato
r systems. \n\nIn this talk\, after presenting an overview of the classica
l problem\, I will discuss an infinite dimensional and continuous setting\
, where finite matrices are replaced by measurable Schur multipliers. I wi
ll first introduce scalar-valued and operator-valued Schur multipliers and
their partially defined versions\, and present a Grothendieck-type charac
terisation of operator-valued Schur multipliers. Then I will talk about th
e positive extension problem of Schur multipliers and characterise its aff
irmative solution in terms of structures on an operator system associated
with the domain of the Schur multipliers.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Osamu Hatori (Niigata University)
DTSTART:20200805T110000Z
DTEND:20200805T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/11
DESCRIPTION:Title: When does an isometry on a Banach algebra preserve the multiplic
ative structure?\nby Osamu Hatori (Niigata University) as part of Pres
erver Webinar\n\n\nAbstract\nThe Banach-Stone theorem asserts that unital
commutative $C^*$-algebras are isometric as Banach spaces if and only if t
hey are isomorphic as Banach algebras.\n\nProblem: For which (commutative)
Banach algebras does the Banach space structures ensure the Banach algebr
a structure?\n\nA theorem of Nagasawa (1959)\, or deLeeuw\, Rudin and Werm
er (1960) states that a surjective complex-linear isometry between uniform
algebras is a weighted composition operator. Hence a uniform algebra sati
sfies the mentioned property in Problem. A standard proof of the theorem d
epends on the so-called extreme point argument. The Arens-Kelley theorem a
sserts that an extreme point of the closed unit ball of the dual space of
a uniform algebra is the point evaluation at a Choquet boundary point foll
owed by a scalar multiplication of the unit modulus. Thus the dual map of
the given isometry gives the correspondence between the Choquet boundaries
\, which induces the composition part of the isometry. It is interesting t
hat\nthe first result on isometries of the Hardy spaces depend on this the
orem.\nOn the other hand\, the dual space of the Wiener algebra $W({\\math
bb T})=\\{f\\in C({\\mathbb T}):\\sum|\\hat{f}(n)|<\\infty\\}$ is $\\ell^\
\infty({\\mathbb Z})$\, and an Arens-Kelley theorem does not hold for the
Wiener algebra. For any bijection $\\varphi$ from the set of the positive
integers onto the set of all integers\, the map $T:W({\\mathbb T})\\to W_+
({\\mathbb T})$ defined by\n\\[\nT(f)(e^{i\\theta})=\\sum_{n=0}^\\infty \\
hat{f}(\\varphi(n))e^{in\\theta}\,\\quad f\\in W({\\mathbb T})\n\\]\nis a
surjective complex-linear isometry\, where\n$W_+({\\mathbb T})=\\{f\\in W(
{\\mathbb T}):\\hat{f}(n)=0\, \\forall n<0\\}$ is a closed subalgebra of $
W({\\mathbb T})$. On the other hand\, $W({\\mathbb T})$ is not algebraical
ly isomorphic as Banach algebra to $W_+({\\mathbb T})$ since the maximal i
deal spaces of these two algebras are not homeomorphic to each other.\nThi
s reminds us that the class of Banach algebras which satisfy the mentioned
property in Problem \nis not so large. The answer to Problem is far from
being completed.\n\nI will give a survey talk concerning to Problem and t
he related subjects such as isometries on spaces of analytic functions.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marten Wortel (University of Pretoria)
DTSTART:20200812T110000Z
DTEND:20200812T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/12
DESCRIPTION:Title: Order isomorphisms between effect algebras of atomic JBW-algebra
s\nby Marten Wortel (University of Pretoria) as part of Preserver Webi
nar\n\n\nAbstract\nIn this talk we will discuss an extension of a recent p
aper by Semrl that characterised order isomorphisms of the effect algebra
(the self-adjoint operators on a Hilbert space between the zero and identi
ty operator) to atomic JBW-algebras. The first part of the talk will be de
voted to giving a brief introduction to Jordan operator algebras\, focussi
ng on the motivations why one would want to consider the more general but
slightly more complicated Jordan setting instead of just the operator alge
bra setting. In the second part of the talk we will explain the ideas behi
nd our proof for the atomic JBW-algebra case.\n\nThis is joint work with M
ark Roelands.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Oikhberg (University of Illinois)
DTSTART:20200819T140000Z
DTEND:20200819T150000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/13
DESCRIPTION:Title: Stability of disjointness preservation\nby Timur Oikhberg (U
niversity of Illinois) as part of Preserver Webinar\n\n\nAbstract\nAn oper
ator $T$ between Banach lattices $E$ and $F$ is said to be $\\varepsilon$-
disjointness preserving ($\\varepsilon$-DP for short) if we have $\\| |Tx|
\\wedge |Ty| \\| \\leq \\varepsilon$ whenever $x$ and $y$ are disjoint el
ements of $E$. $0$-DP operators are simply called disjointness preserving\
, or DP for short. One can easily show that\, if $T$ is DP\, then $S$ is $
3\\|T-S\\|$-DP. We are interested in the converse of this statement: if $T
$ is $\\varepsilon$-DP\, must it be a small perturbation of a DP operator?
In many cases\, the answer is positive\; however\, some counterexamples a
lso exist.\n\nWe also consider stability of some related properties for Ba
nach lattices\, as well as similar questions in the non-commutative settin
g.\n\nThis is a joint work with P.Tradacete.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ngai-Ching Wong (National Sun Yat-sen University)
DTSTART:20200826T110000Z
DTEND:20200826T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/14
DESCRIPTION:Title: Disjointness preservers of operator algebras\nby Ngai-Ching
Wong (National Sun Yat-sen University) as part of Preserver Webinar\n\n\nA
bstract\nI will report my 25 year struggle with the problem of whether a l
inear disjointness preserver\n$T$ between two C*-algebras $A$ and $B$ is c
lose to an algebra/Jordan (*-)homomorphism. \nHere\, the disjointness of t
wo elements $a\, b$ in a C*-algebra can have at least 5 versions\; namely\
,\n\n$$ab = 0\, a^*b=0\, ab^*=0\, a^*b=ab^*=0\, \\text{ or } ab=ba=0.$$\n\
nWhen $a\,b$ are self-adjoint\, all reduce to the zero product case $ab=0$
.\nFor example\, we ask what happens if $T$ preserves zero products.\n\nWe
attack the problem in several steps.\n\nIt is pretty fruitful when $A\,B$
are commutative C*-algebras.\nIt is also satisfactory when $A\,B$ are mat
rix algebras.\nIn both cases\, a linear zero product preserver $T: A\\to B
$ is merely a direct sum\nof a good part $hJ$ and a `bad but small' part.\
nHere\, $h$ is a central element affiliated with $B$\, and $J$ is a Jordan
homomorphism.\nThe bad part arises either from the discontinuity\, or the
non-surjectivity of $T$ which\ntranslates into that the range $TA$ is not
a C*-algebra.\n\nIn general\, we need to assume either the continuity or
the surjectivity of $T$.\nWhen $T$ is a continuous linear disjointness pre
server\, we have a quite complete answer.\nIt merely says that $T=hJ$ is a
lmost good.\n\nFor a surjective linear disjointness preserver $T: A\\to B$
\,\nwe have good answers for the cases when $A\,B$ are W*-algebras or AW*-
algebras.\nThe solutions are obtained by decomposing $T$ as a direct sum o
f surjective linear disjointness\npreservers between the abelian summands
and between the orthogonal complements. While the abelian\npart involves
mainly topological arguments\, the nonabelian part relies on techniques de
aling with projections.\n\nThe major obstruction to carry on to the C*-alg
ebra case is due to the lack\nof nontrivial projections for general C*-alg
ebras. We managed to finish the cases\nwhen $A\, B$ are type I or properl
y infinite. \nFor a complete answer\, we devote a great efforts to the dev
eloping of\ntwo type decomposition theories for general C*-algebras\, so t
hat any C*-algebra $A$ has\nan essential ideal which is a direct sum of ty
pe A finite\, type A infinite\, type B finite\, type B infinite\,\nand typ
e C. Our plan is to solve the problem for surjective linear disjointness
preservers between C*-algebras\nof each of these 5 types\, and `glue' the
5 versions together for a complete answer. \nUnfortunately\, we have encou
ntered big difficulties and struck for some years.\n\nWe have also worked
on other preserver problems for motivations\, \ne.g. linear orthogonality
preservers of Hilbert C*-modules\, and orthogonal additive conformal disjo
intness preservers of C*-algebras.\n\nIn this talk\, I will present some d
etails of the above experience.\nThe above works are contributions of many
authors. Some of them are in the audience\, for example\,\nChi-Kwong Li\
, Lajos Molnar and Antonio Peralta\, as well as some of my long time colla
borators\, \nChi-Wai Leung\, Lei Li\, Chi-Keung Ng\, Ming-Cheng Tsai and Y
a-Shu Wang\, to name a few.\n\nI hope the audience can help to solve the p
roblem.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Haonan Zhang (IST Austria)
DTSTART:20200902T110000Z
DTEND:20200902T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/15
DESCRIPTION:Title: Data processing inequalities for alpha-z Rényi relative entropi
es and the equality conditions\nby Haonan Zhang (IST Austria) as part
of Preserver Webinar\n\n\nAbstract\nData processing inequality for quantum
relative entropy is a fundamental inequality in quantum information theor
y. The alpha-z Rényi relative entropies are a two-parameter family of qua
ntum Rényi relative entropies. In this talk we give the full range of the
parameters (alpha\,z) for which the data processing inequalities are vali
d and discuss their equality conditions. Along the way we review the resul
ts of joint convexity/concavity of certain trace functionals\, and prove a
conjecture of Audenaert and Datta and a conjecture of Carlen\, Frank and
Lieb.\n\nThe talk is based on two papers arXiv:1811.01205 and arXiv:2007.0
6644.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Pankov (University of Warmia & Mazury\, Poland and Johannes K
epler Universität Linz\, Austria)
DTSTART:20200916T110000Z
DTEND:20200916T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/16
DESCRIPTION:Title: A geometric approach to Wigner-type theorems\nby Mark Pankov
(University of Warmia & Mazury\, Poland and Johannes Kepler Universität
Linz\, Austria) as part of Preserver Webinar\n\n\nAbstract\nLet $H$ be a c
omplex Hilbert space and let ${\\mathcal P}(H)$ be the associated projecti
ve space (the set of rank-one projections). Suppose that $\\dim H\\ge 3$.
We prove the following Wigner-type theorem: if $H$ is finite-dimensional\,
then an arbitrary orthogonality preserving\ntransformation of ${\\mathcal
P}(H)$ (i.e. sending orthogonal projections to orthogonal projections\nwi
thout the assumption that the orthogonality relation is preserved in both
directions) is induced by a unitary or anti-unitary operator. In the case
when $H$ is infinite-dimensional\, this fails.\n\nThe problem is reduced t
o a description of orthogonality preserving\nlineations. Lineations are ma
ps between projective spaces which send lines to\nsubsets of lines. In gen
eral\, the behavior of lineations is complicated\;\nthey are not injective
and can send lines to parts of lines only.\n\nOur version of Wigner's the
orem is a consequence of the following\nresult:\nevery orthogonality prese
rving lineation of ${\\mathcal P}(V)$ to itself\nis induced by\na linear o
r conjugate-linear isometry\n(now\, we do not require that $H$ is finite-d
imensional).\n\nAs an application\, we describe (not necessarily injectiv
e)\ntransformations of Grassmannians preserving\nsome types of principal a
ngles.\n\nThis is a joint work with Thomas Vetterlein.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dijana Ilisevic (University of Zagreb\, Croatia)
DTSTART:20200930T110000Z
DTEND:20200930T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/17
DESCRIPTION:Title: An inverse eigenvalue problem for isometries\nby Dijana Ilis
evic (University of Zagreb\, Croatia) as part of Preserver Webinar\n\n\nAb
stract\nThis talk is related to the following problem: when is a given fin
ite set of modulus one complex numbers the spectrum of a linear isometry o
n a complex Banach space? Necessary conditions on such a set will be prese
nted. Since sufficient conditions are related to the structure of specific
Banach spaces\, some particular cases will be considered and insightful e
xamples will be given.\n\nThe core of this talk is based on the paper On i
sometries with finite spectrum\, written jointly with Fernanda Botelho\, a
ccepted for publication in the Journal of Operator Theory.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miklós Pálfia (Sungkyunkwan University\, Republic of Korea)
DTSTART:20201021T110000Z
DTEND:20201021T120000Z
DTSTAMP:20260404T084904Z
UID:PreserverWebinar/18
DESCRIPTION:Title: Analytic lifts of operator monotone and concave functions\nb
y Miklós Pálfia (Sungkyunkwan University\, Republic of Korea) as part of
Preserver Webinar\n\n\nAbstract\nIn the context of free function theory\,
we review recent results on operator monotone and concave functions in se
veral variables. In particular we study the connection between operator mo
notonicity and concavity on certain domains. It turns out\, that on positi
ve operators monotonicity and concavity are equivalent. Thus we exploit th
is to construct a non-commutative analytic lift for partially defined func
tions such as multivariable real functions that are either operator monoto
ne or operator concave. These results can also be applied in more general
settings\, like in the case of operator means of probability measures.\n\n
We will also study a version of monotonicity with respect to the real posi
tive definite order introduced recently by Blecher. It turns out that the
real parts of such functions are completely characterizable by operator mo
notone functions. Moreover if the function is assumed to be free analytic\
, then it must be affine linear. This latter part of the talk is based on
a joint work with Marcell Gaál.\n
LOCATION:https://researchseminars.org/talk/PreserverWebinar/18/
END:VEVENT
END:VCALENDAR