On Banach spaces whose group of isometrics acts micro-transitively on the unit sphere
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
On Banach spaces whose group of isometrics acts micro-transitively on the unit sphere
Original language description
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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
1096-0813
Volume of the periodical
488
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
14
Pages from-to
1-14
UT code for WoS article
000525911000008
EID of the result in the Scopus database
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