When is a locally convex space Eberlein-Grothendieck?

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00563646" target="_blank" >RIV/67985840:_____/22:00563646 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00025-022-01770-w" target="_blank" >https://doi.org/10.1007/s00025-022-01770-w</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00025-022-01770-w" target="_blank" >10.1007/s00025-022-01770-w</a>

Jazyk výsledku

angličtina

Název v původním jazyce

When is a locally convex space Eberlein-Grothendieck?

Popis výsledku v původním jazyce

The weak topology of a locally convex space (lcs) E is denoted by w. In this paper we undertake a systematic study of those lcs E such that (E, w) is (linearly) Eberlein-Grothendieck (see Definitions 1.2 and 3.1). The following results obtained in our paper play a key role: for every barrelled lcs E, the space (E, w) is Eberlein-Grothendieck (linearly Eberlein-Grothendieck) if and only if E is metrizable (E is normable, respectively). The main applications concern to the space of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology Ck(X). We prove that (Ck(X) , w) is Eberlein-Grothendieck (linearly Eberlein-Grothen-dieck) if and only if X is hemicompact (X is compact, respectively). Besides this, we show that the class of E for which (E, w) is linearly Eberlein-Grothendieck preserves linear continuous quotients. Various illustrating examples are provided.

Název v anglickém jazyce

When is a locally convex space Eberlein-Grothendieck?

Popis výsledku anglicky

The weak topology of a locally convex space (lcs) E is denoted by w. In this paper we undertake a systematic study of those lcs E such that (E, w) is (linearly) Eberlein-Grothendieck (see Definitions 1.2 and 3.1). The following results obtained in our paper play a key role: for every barrelled lcs E, the space (E, w) is Eberlein-Grothendieck (linearly Eberlein-Grothendieck) if and only if E is metrizable (E is normable, respectively). The main applications concern to the space of continuous real-valued functions on a Tychonoff space X endowed with the compact-open topology Ck(X). We prove that (Ck(X) , w) is Eberlein-Grothendieck (linearly Eberlein-Grothen-dieck) if and only if X is hemicompact (X is compact, respectively). Besides this, we show that the class of E for which (E, w) is linearly Eberlein-Grothendieck preserves linear continuous quotients. Various illustrating examples 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

Results in Mathematics

ISSN

1422-6383

e-ISSN

1420-9012

Svazek periodika

77

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

16

Strana od-do

236

Kód UT WoS článku

000873856800003

EID výsledku v databázi Scopus

2-s2.0-85140615299