On Banach spaces whose group of isometrics acts micro-transitively on the unit sphere

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F20%3A00346268" target="_blank" >RIV/68407700:21230/20:00346268 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jmaa.2020.124046" target="_blank" >https://doi.org/10.1016/j.jmaa.2020.124046</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2020.124046" target="_blank" >10.1016/j.jmaa.2020.124046</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On Banach spaces whose group of isometrics acts micro-transitively on the unit sphere

Popis výsledku v původním jazyce

We study Banach spaces whose group of isometrics acts micro-transitively on the unit sphere. We introduce a weaker property, inherited by one-complemented subspaces, that we call uniform micro-semitransitivity. We prove a number of results about both micro-transitive and uniformly micro-semitransitive spaces. In particular, they are uniformly convex and uniformly smooth, and form a self-dual class. To this end, we relate the fact that the group of isometrics acts micro-transitively with a property of operators called the pointwise Bishop-Phelps-Bollobas property and use some known results on it. Besides, we show that if there is a non-Hilbertian non-separable Banach space with uniform micro-semitransitive (or micro-transitive) norm, then there is a non-Hilbertian separable one. Finally, we show that an L-p(mu) space is micro-transitive or uniformly micro-semitransitive only when p = 2. (C) 2020 Elsevier Inc. All rights reserved.

Název v anglickém jazyce

On Banach spaces whose group of isometrics acts micro-transitively on the unit sphere

Popis výsledku anglicky

We study Banach spaces whose group of isometrics acts micro-transitively on the unit sphere. We introduce a weaker property, inherited by one-complemented subspaces, that we call uniform micro-semitransitivity. We prove a number of results about both micro-transitive and uniformly micro-semitransitive spaces. In particular, they are uniformly convex and uniformly smooth, and form a self-dual class. To this end, we relate the fact that the group of isometrics acts micro-transitively with a property of operators called the pointwise Bishop-Phelps-Bollobas property and use some known results on it. Besides, we show that if there is a non-Hilbertian non-separable Banach space with uniform micro-semitransitive (or micro-transitive) norm, then there is a non-Hilbertian separable one. Finally, we show that an L-p(mu) space is micro-transitive or uniformly micro-semitransitive only when p = 2. (C) 2020 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)

Rok uplatnění

2020

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

488

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

1-14

Kód UT WoS článku

000525911000008

EID výsledku v databázi Scopus

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