Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F23%3A00367883" target="_blank" >RIV/68407700:21230/23:00367883 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2023.127276" target="_blank" >https://doi.org/10.1016/j.jmaa.2023.127276</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2023.127276" target="_blank" >10.1016/j.jmaa.2023.127276</a>
Alternative languages
Result language
angličtina
Original language name
Renormings preserving local geometry at countably many points in spheres of Banach spaces and applications
Original language description
We develop tools to produce equivalent norms with specific local geometry around infinitely many points in the sphere of a Banach space via an inductive procedure. We combine this process with smoothness results and techniques to solve two open problems posed in the recently published monograph [7] by A. J. Guirao, V. Montesinos and V. Zizler. Specifically, on the one hand we construct in every separable Banach space admitting a Ck-smooth norm an equivalent norm which is Ck-smooth but fails to be uniformly Gateaux in any direction; and on the other hand we produce in c0(Gamma) for any infinite Gamma a C infinity-smooth norm whose ball is dentable but whose sphere lacks any extreme points.(c) 2023 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/GA23-04776S" target="_blank" >GA23-04776S: Interplay of algebraic, metric, geometric and topological structures on Banach spaces</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2023
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
526
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
17
Pages from-to
127276-127292
UT code for WoS article
000972103800001
EID of the result in the Scopus database
2-s2.0-85151372265