Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Banach spaces with small weakly open subsets of the unit ball and massive sets of Daugavet and Δ-points

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas

ISSN

1578-7303

e-ISSN

1579-1505

Svazek periodika

118

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

17

Strana od-do

—

Kód UT WoS článku

001206316900001

EID výsledku v databázi Scopus

2-s2.0-85191074647