A characterization of the weak topology in the unit ball of purely atomic L-1 preduals

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F22%3A00360217" target="_blank" >RIV/68407700:21230/22:00360217 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2022.126311" target="_blank" >https://doi.org/10.1016/j.jmaa.2022.126311</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2022.126311" target="_blank" >10.1016/j.jmaa.2022.126311</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A characterization of the weak topology in the unit ball of purely atomic L-1 preduals

Popis výsledku v původním jazyce

We study Banach spaces with a weak stable unit ball, that is, Banach spaces where every convex combination of relatively weakly open subsets in its unit ball is again a relatively weakly open subset in its unit ball. It is proved that the class of L-1 preduals with a weak stable unit ball agree with those L-1 preduals which are purely atomic, that is preduals of l(1)(Gamma) for some set Gamma, getting in this way a complete geometrical characterization of purely atomic preduals of L-1, which answers a setting problem. As a consequence, we prove the equivalence for L-1 preduals of different properties previously studied by other authors, in terms of slices around weak stability. Also we get the weak stability of the unit ball of C-0 (K, X) whenever K is a Hausdorff and scattered locally compact space and X has a norm stable and weak stable unit ball. This gives a characterization of weak stability of the unit ball in C-0 (K, X) for finite-dimensional X. Finally we prove that Banach spaces with a weak stable unit ball satisfy a very strong new version of diameter two property. (C) 2022 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

A characterization of the weak topology in the unit ball of purely atomic L-1 preduals

Popis výsledku anglicky

We study Banach spaces with a weak stable unit ball, that is, Banach spaces where every convex combination of relatively weakly open subsets in its unit ball is again a relatively weakly open subset in its unit ball. It is proved that the class of L-1 preduals with a weak stable unit ball agree with those L-1 preduals which are purely atomic, that is preduals of l(1)(Gamma) for some set Gamma, getting in this way a complete geometrical characterization of purely atomic preduals of L-1, which answers a setting problem. As a consequence, we prove the equivalence for L-1 preduals of different properties previously studied by other authors, in terms of slices around weak stability. Also we get the weak stability of the unit ball of C-0 (K, X) whenever K is a Hausdorff and scattered locally compact space and X has a norm stable and weak stable unit ball. This gives a characterization of weak stability of the unit ball in C-0 (K, X) for finite-dimensional X. Finally we prove that Banach spaces with a weak stable unit ball satisfy a very strong new version of diameter two property. (C) 2022 Elsevier Inc. All rights reserved.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

514

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

000832042900008

EID výsledku v databázi Scopus

2-s2.0-85130405367