On dual Kadec norms

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389450" target="_blank" >RIV/68407700:21230/25:00389450 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jfa.2024.110698" target="_blank" >https://doi.org/10.1016/j.jfa.2024.110698</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jfa.2024.110698" target="_blank" >10.1016/j.jfa.2024.110698</a>

Result language
angličtina
Original language name
On dual Kadec norms
Original language description
Let ( X, ||center dot||) be a Banach space such that all w*-convergent sequences in the dual unit sphere S-X* are also norm convergent. Then the weak* and norm topologies agree on S-X*. By known results it implies that X has a renorming whose dual is locally uniformly rotund, hence also C 1-Frechet smooth. In particular, X is an Asplund space. Our results also lend an alternative proof of the celebrated Josefson-Nissenzweig theorem.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

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)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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