Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21240%2F24%3A00377165" target="_blank" >RIV/68407700:21240/24:00377165 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s13398-024-01596-x" target="_blank" >https://doi.org/10.1007/s13398-024-01596-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s13398-024-01596-x" target="_blank" >10.1007/s13398-024-01596-x</a>
Alternative languages
Result language
angličtina
Original language name
Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points
Original language description
We prove that there exists an equivalent norm . on Linfinity[0,1] with the following properties: The unit ball of (Linfinity[0,1],.) contains non-empty relatively weakly open subsets of arbitrarily small diameter; The set of Daugavet points of the unit ball of (Linfinity[0,1],.) is weakly dense; The set of ccw Δ-points of the unit ball of (Linfinity[0,1],.) is norming. We also show that there are points of the unit ball of (Linfinity[0,1],.) which are not Δ-points, meaning that the space (Linfinity[0,1],.) fails the diametral local diameter 2 property. Finally, we observe that the space (Linfinity[0,1],.) provides both alternative and new examples that illustrate the differences between the various diametral notions for points of the unit ball of Banach spaces.
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSN
1578-7303
e-ISSN
1579-1505
Volume of the periodical
118
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
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UT code for WoS article
001206316900001
EID of the result in the Scopus database
2-s2.0-85191074647