Feral dual spaces and (strongly) distinguished spaces C(X)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00571369" target="_blank" >RIV/67985840:_____/23:00571369 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s13398-023-01417-7" target="_blank" >https://doi.org/10.1007/s13398-023-01417-7</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13398-023-01417-7" target="_blank" >10.1007/s13398-023-01417-7</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Feral dual spaces and (strongly) distinguished spaces C(X)

Popis výsledku v původním jazyce

Following Dieudonné and Schwartz a locally convex space is distinguished if its strong dual is barrelled. The distinguished property for spaces Cp(X) of continuous real-valued functions over a Tychonoff space X is a peculiar (although applicable) property. It is known that Cp(X) is distinguished if and only if Cp(X) is large in RX if and only if X is a Δ -space (in sense of Reed) if and only if the strong dual of Cp(X) carries the finest locally convex topology. Our main results about spaces whose strong dual has only finite-dimensional bounded sets (see Theorems 2, 7 and Proposition 4) are used to study distinguished spaces Ck(X) with the compact-open topology. We also put together several known facts (Theorem 6) about distinguished spaces Cp(X) with self-contained full proofs.

Název v anglickém jazyce

Feral dual spaces and (strongly) distinguished spaces C(X)

Popis výsledku anglicky

Following Dieudonné and Schwartz a locally convex space is distinguished if its strong dual is barrelled. The distinguished property for spaces Cp(X) of continuous real-valued functions over a Tychonoff space X is a peculiar (although applicable) property. It is known that Cp(X) is distinguished if and only if Cp(X) is large in RX if and only if X is a Δ -space (in sense of Reed) if and only if the strong dual of Cp(X) carries the finest locally convex topology. Our main results about spaces whose strong dual has only finite-dimensional bounded sets (see Theorems 2, 7 and Proposition 4) are used to study distinguished spaces Ck(X) with the compact-open topology. We also put together several known facts (Theorem 6) about distinguished spaces Cp(X) with self-contained full proofs.

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

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales

ISSN

1578-7303

e-ISSN

1579-1505

Svazek periodika

117

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

94

Kód UT WoS článku

000963878200001

EID výsledku v databázi Scopus

2-s2.0-85152537442