On Asplund spaces Ck(X) and w∗-binormality
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575131" target="_blank" >RIV/67985840:_____/23:00575131 - isvavai.cz</a>
Výsledek na webu
<a href="https://doi.org/10.1007/s00025-023-01979-3" target="_blank" >https://doi.org/10.1007/s00025-023-01979-3</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-023-01979-3" target="_blank" >10.1007/s00025-023-01979-3</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
On Asplund spaces Ck(X) and w∗-binormality
Popis výsledku v původním jazyce
A celebrated theorem of Namioka and Phelps (Duke Math. J. 42:735-750, 1975) says that for a compact space X, the Banach space C(X) is Asplund iff X is scattered. In our paper we extend this result to the space of continuous real-valued functions endowed with the compact-open topology Ck(X) for several natural classes of non-compact Tychonoff spaces X. The concept of Δ 1-spaces introduced recently in Ka̧kol et al. (Some classes of topological spaces extending the class of Δ -spaces, submitted for publication) has been shown to be applicable for this research. w∗-binormality of the dual of the Banach space C(X) implies that C(X) is Asplund (Kurka in J Math Anal Appl 371:425–435, 2010). In our paper we prove in particular that for a Corson compact space X the converse is true. We establish a tight relationship between the property of w∗-binormality of the dual C(X) ′ and the class of compact Δ-spaces X introduced and explored earlier in Ka̧kol and Leiderman (Proc. Am. Math. Soc. Ser B 8:86-99, 2021, 8:267-280, 2021). We find a complete characterization of a compact space X such that the dual C(X)′ possesses a stronger property called effective w∗ -binormality. We provide several illustrating examples and pose open questions.
Název v anglickém jazyce
On Asplund spaces Ck(X) and w∗-binormality
Popis výsledku anglicky
A celebrated theorem of Namioka and Phelps (Duke Math. J. 42:735-750, 1975) says that for a compact space X, the Banach space C(X) is Asplund iff X is scattered. In our paper we extend this result to the space of continuous real-valued functions endowed with the compact-open topology Ck(X) for several natural classes of non-compact Tychonoff spaces X. The concept of Δ 1-spaces introduced recently in Ka̧kol et al. (Some classes of topological spaces extending the class of Δ -spaces, submitted for publication) has been shown to be applicable for this research. w∗-binormality of the dual of the Banach space C(X) implies that C(X) is Asplund (Kurka in J Math Anal Appl 371:425–435, 2010). In our paper we prove in particular that for a Corson compact space X the converse is true. We establish a tight relationship between the property of w∗-binormality of the dual C(X) ′ and the class of compact Δ-spaces X introduced and explored earlier in Ka̧kol and Leiderman (Proc. Am. Math. Soc. Ser B 8:86-99, 2021, 8:267-280, 2021). We find a complete characterization of a compact space X such that the dual C(X)′ possesses a stronger property called effective w∗ -binormality. We provide several illustrating examples and pose open questions.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.
Návaznosti
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Ostatní
Rok uplatnění
2023
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Svazek periodika
78
Číslo periodika v rámci svazku
5
Stát vydavatele periodika
DE - Spolková republika Německo
Počet stran výsledku
19
Strana od-do
203
Kód UT WoS článku
001045166300001
EID výsledku v databázi Scopus
2-s2.0-85168273160