Skip to content

Author: Anna Pelczar-Barwacz

2024.03.20 Taras Banakh

Published 22/03/2024

Ivan Franko National University of Lviv and Jan Kochanowski University of Kielce

Geometry of Banakh spaces

Abstract: Following Will Brian, we define a metric space X to be Banakh if all nonempty spheres of positive radius r in X have cardinality 2 and diameter 2r. This notion arose from attempts to find a characterization of the real line in the class of metric spaces. Standard examples of Banakh spaces are subgroups of the real line. However, there exist also some exotic examples of Banakh spaces that are quite different from subsets of the real line. In particular, every Hilbert space of density less or equal to the continuum contains a dense Banakh subgroup.

Leave a Comment

Michał Popow

Published 02/03/2024

Pomeranian University in Słupsk (Poland) and Vasyl Stefanyk Precarpathian National University, IvanoFrankivsk (Ukraine)

Representation theorems for regular operators

[6.03.2024, 12.15] 

[THE MEETING IS HELD ONLINE ONLY]

Please find the abstract here

Join the meeting here.

Leave a Comment

Antoni Machowski

Published 15/02/2024

Jagiellonian University 

Strongly exposing functionals of convex weakly compact sets

[27.02.2024, 12.15. THE MEETING IS HELD HYBRID, STATIONARY PART in 1016]

Abstract: For a closed, convex bounded subset C of a Banach space X we call a point x in C strongly exposed if some functional on X attains its strong maximum in x. Functionals of norm one that satisfy the above condition for some point in C are called strongly exposing functionals of C. In my talk I will present a proof by J. Bourgain of celebrated results by J. Lindenstrauss and S.L. Troyanski stating that a convex and weakly compact subset of a Banach space is the closed convex hull of its strongly exposed points and the set of strongly exposing functionals of C is a dense G-delta subset of the unit sphere of X*.

References:

J. Lindenstrauss, On operators which attain their norm (1963)

S. L. Trojanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces (1970)

J. Bourgain, Strongly exposed points in weakly compact convex sets in Banach spaces (1976)

Join the meeting now

Meeting ID: 392 359 686 95

Passcode: HMgHLn

Leave a Comment

Seminars in 2023/2034 (Winter term)

Published 06/02/2024
24.01.2024 ▴ Jerzy Grzybowski (Adam Mickiewicz University in Poznań):
Maksymalna różnica Demyanova zbiorów wypukłych, a maksymalna ilość punktów ekstremalnych sumy Minkowskiego
 
10.01.2024 ▴ Tomasz Kania:
Lattice points in Banach spaces
 
20.12.2023 ▴ Joanna Garbulińska-Węgrzyn (Jan Kochanowski University of Kielce):
On the Darji Matheron universal operator
 
13.12.2023 ▴ Tomasz Kobos:
Spaces with maximal projection constants revisited
 
6.12.2023 ▴ Mariusz Niwiński:
Indefinite inner product spaces and Dirac operators
 
29.11.2023 ▴ Grzegorz Lewicki:
On two-strongly unique best approximation in the complex case
 
22.11.2023 ▴ Anna Pelczar-Barwacz:
Equivalence of block sequences in Schreier spaces
 
8.11.2023 ▴ Krystian Kazaniecki (Johannes Kepler University Linz):
Schur property for jump parts of gradient measures
 
25.10.2023 ▴ Grzegorz Lewicki:
On the maximal hyperplane in ℓ^p_n
 
18.10.2023 ▴ Hanna Wojewódka-Ściążko (UŚ; PAN):
When asymptotically stable Markov semigroups have the e-property?
 
11.10.2023 ▴ Jerzy Kąkol:
About Banach-Mazur’s problem from the 1930s
 
4.10.2023 ▴ Michał Wojciechowski (Instytut Matematyczny Polskiej Akademii Nauk):
Singular pluriharmonic quaternionic measure
 
Leave a Comment

Seminars in 2022/2023

Published 06/02/2024
31.05.2023  Tomasz Kochanek (MIMUW):
The Hyers-Ulam property of groups and its connections to group C*-algebras
 
24.05.2023  Tomasz Kobos:
Lower bounds on the norm of linear projection through smoothness
 
17.05.2023  Antoni Machowski:
A generalization of a theorem of Yamabe
 
10.05.2023  Jarosław Swaczyna (Technical University of Łódź):
Slow dynamical systems with large Hausdorff dimension
 
26.04.2023  Anna Pelczar-Barwacz:
Operator ideals on Schreier spaces of arbitrary order
 
19.04.2023  Natalia Maślany (UJ):
Differential embeddings into algebras of topological stable rank 1
 
5.04.2023  Barbara Lewandowska:
On the generalized Grunbaum conjecture (2)
 
22.03.2023  Barbara Lewandowska:
On the generalized Grunbaum conjecture (1)
 
8.03.2023  Tomasz Kobos:
An affine dimension of the set of minimal hyperplane projections
 
25.01.2023  Tomasz Kania:
Isometries of combinatorial Tsirelson spaces
 
18.01.2023  Grzegorz Lewicki:
Minimal projections onto subspaces generated by sign matrices (2)
 
11.01.2023  Grzegorz Lewicki:
Minimal projections onto subspaces generated by sign matrices (1)
 
14.12.2022  Krzysztof Ciosmak (University of Oxford, Fields Institute, University of Toronto):
Multi-dimensional localisation and 1-Lipschitz maps
 
7.12.2022  Natalia Maślany:
Isometries of combinatorial Tsirelson spaces
 
30.11.2022  Tomasz Kobos:
On the affine dimension of the set of minimal projections (4)
 
23.11.2022  Tomasz Kobos:
On the affine dimension of the set of minimal projections (3)
 
16.11.2022  Bence Horváth (Institute of Mathematics of the Czech Academy of Sciences):
Ring-theoretic (in)finiteness in ultraproducts of Banach algebras
 
9.11.2022  Anna Pelczar-Barwacz:
A Banach space with an infinite-dimensional reflexive quotient algebra L(X)/SS(X)
 
26.10.2022  Tomasz Kobos:
On the affine dimension of the set of minimal projections (2)
 
19.10.2022  Andrzej Kryczka (UMCS):
Regularne metody sumowania dla sum prostych i przestrzeni interpolacyjnych
 
12.10.2022  Tomasz Kobos:
On the affine dimension of the set of minimal projections (1)
 
5.10.2022  Spotkanie organizacyjne 
Leave a Comment