omega(omega)-base and infinite-dimensional compact sets in locally convex spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00557877" target="_blank" >RIV/67985840:_____/22:00557877 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s13163-021-00397-9" target="_blank" >https://doi.org/10.1007/s13163-021-00397-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13163-021-00397-9" target="_blank" >10.1007/s13163-021-00397-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

omega(omega)-base and infinite-dimensional compact sets in locally convex spaces

Popis výsledku v původním jazyce

A locally convex space (lcs) E is said to have an ωω-base if E has a neighborhood base { Uα: α∈ ωω} at zero such that Uβ⊆ Uα for all α≤ β. The class of lcs with an ωω-base is large, among others contains all (LM)-spaces (hence (LF)-spaces), strong duals of distinguished Fréchet lcs (hence spaces of distributions D′(Ω)). A remarkable result of Cascales-Orihuela states that every compact set in an lcs with an ωω-base is metrizable. Our main result shows that every uncountable-dimensional lcs with an ωω-base contains an infinite-dimensional metrizable compact subset. On the other hand, the countable-dimensional vector space φ endowed with the finest locally convex topology has an ωω-base but contains no infinite-dimensional compact subsets. It turns out that φ is a unique infinite-dimensional locally convex space which is a kR-space containing no infinite-dimensional compact subsets. Applications to spaces Cp(X) are provided.

Název v anglickém jazyce

omega(omega)-base and infinite-dimensional compact sets in locally convex spaces

Popis výsledku anglicky

A locally convex space (lcs) E is said to have an ωω-base if E has a neighborhood base { Uα: α∈ ωω} at zero such that Uβ⊆ Uα for all α≤ β. The class of lcs with an ωω-base is large, among others contains all (LM)-spaces (hence (LF)-spaces), strong duals of distinguished Fréchet lcs (hence spaces of distributions D′(Ω)). A remarkable result of Cascales-Orihuela states that every compact set in an lcs with an ωω-base is metrizable. Our main result shows that every uncountable-dimensional lcs with an ωω-base contains an infinite-dimensional metrizable compact subset. On the other hand, the countable-dimensional vector space φ endowed with the finest locally convex topology has an ωω-base but contains no infinite-dimensional compact subsets. It turns out that φ is a unique infinite-dimensional locally convex space which is a kR-space containing no infinite-dimensional compact subsets. Applications to spaces Cp(X) are provided.

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

2022

Kód důvěrnosti údajů

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

Název periodika

Revista Mathématica Complutense

ISSN

1139-1138

e-ISSN

1988-2807

Svazek periodika

35

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

16

Strana od-do

599-614

Kód UT WoS článku

000652075100001

EID výsledku v databázi Scopus

2-s2.0-85106217998