Grothendieck C(K)-spaces and the Josefson-Nissenzweig theorem

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00579686" target="_blank" >RIV/67985840:_____/23:00579686 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.4064/fm218-6-2023" target="_blank" >https://doi.org/10.4064/fm218-6-2023</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4064/fm218-6-2023" target="_blank" >10.4064/fm218-6-2023</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Grothendieck C(K)-spaces and the Josefson-Nissenzweig theorem

Popis výsledku v původním jazyce

For a compact space K, the Banach space C(K) is said to have the l(1)-Grothendieck property if every weak* convergent sequence (mu(n) : n is an element of omega) of functionals on C(K) such that mu(n) is an element of l(1)(K) for every n is an element of omega is weakly convergent. Thus, the l(1)- Grothendieck property is a weakening of the standard Grothendieck property for Banach spaces of continuous functions. We observe that C(K) has the l(1)-Grothendieck property if and only if there does not exist any sequence of functionals (mu(n) : n is an element of omega) on C(K), with mu(n) is an element of l(1)(K) for every n is an element of omega, satisfying the conclusion of the classical Josefson-Nissenzweig theorem. We construct an example of a separable compact space K such that C(K) has the l(1)-Grothendieck property but it does not have the Grothendieck property. We also show that for many classical consistent examples of Efimov spaces K their Banach spaces C(K) do not have the l(1)-Grothendieck property.

Název v anglickém jazyce

Grothendieck C(K)-spaces and the Josefson-Nissenzweig theorem

Popis výsledku anglicky

For a compact space K, the Banach space C(K) is said to have the l(1)-Grothendieck property if every weak* convergent sequence (mu(n) : n is an element of omega) of functionals on C(K) such that mu(n) is an element of l(1)(K) for every n is an element of omega is weakly convergent. Thus, the l(1)- Grothendieck property is a weakening of the standard Grothendieck property for Banach spaces of continuous functions. We observe that C(K) has the l(1)-Grothendieck property if and only if there does not exist any sequence of functionals (mu(n) : n is an element of omega) on C(K), with mu(n) is an element of l(1)(K) for every n is an element of omega, satisfying the conclusion of the classical Josefson-Nissenzweig theorem. We construct an example of a separable compact space K such that C(K) has the l(1)-Grothendieck property but it does not have the Grothendieck property. We also show that for many classical consistent examples of Efimov spaces K their Banach spaces C(K) do not have the l(1)-Grothendieck property.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF20-22230L" target="_blank" >GF20-22230L: Banachovy prostory spojitých a lipschitzovských funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Fundamenta Mathematicae

ISSN

0016-2736

e-ISSN

1730-6329

Svazek periodika

263

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

PL - Polská republika

Počet stran výsledku

27

Strana od-do

105-131

Kód UT WoS článku

001108631400001

EID výsledku v databázi Scopus

2-s2.0-85179096168