On linear continuous operators between distinguished spaces Cp(X)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00546784" target="_blank" >RIV/67985840:_____/21:00546784 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s13398-021-01121-4" target="_blank" >https://doi.org/10.1007/s13398-021-01121-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s13398-021-01121-4" target="_blank" >10.1007/s13398-021-01121-4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On linear continuous operators between distinguished spaces Cp(X)

Popis výsledku v původním jazyce

As proved in Ka̧kol and Leiderman (Proc AMS Ser B 8:86–99, 2021), for a Tychonoff space X, a locally convex space Cp(X) is distinguished if and only if X is a Δ -space. If there exists a linear continuous surjective mapping T: Cp(X) → Cp(Y) and Cp(X) is distinguished, then Cp(Y) also is distinguished (Ka̧kol and Leiderman Proc AMS Ser B, 2021). Firstly, in this paper we explore the following question: Under which conditions the operator T: Cp(X) → Cp(Y) above is open? Secondly, we devote a special attention to concrete distinguished spaces Cp([1 , α]) , where α is a countable ordinal number. A complete characterization of all Y which admit a linear continuous surjective mapping T: Cp([1 , α]) → Cp(Y) is given. We also observe that for every countable ordinal α all closed linear subspaces of Cp([1 , α]) are distinguished, thereby answering an open question posed in Ka̧kol and Leiderman (Proc AMS Ser B, 2021).

Název v anglickém jazyce

On linear continuous operators between distinguished spaces Cp(X)

Popis výsledku anglicky

As proved in Ka̧kol and Leiderman (Proc AMS Ser B 8:86–99, 2021), for a Tychonoff space X, a locally convex space Cp(X) is distinguished if and only if X is a Δ -space. If there exists a linear continuous surjective mapping T: Cp(X) → Cp(Y) and Cp(X) is distinguished, then Cp(Y) also is distinguished (Ka̧kol and Leiderman Proc AMS Ser B, 2021). Firstly, in this paper we explore the following question: Under which conditions the operator T: Cp(X) → Cp(Y) above is open? Secondly, we devote a special attention to concrete distinguished spaces Cp([1 , α]) , where α is a countable ordinal number. A complete characterization of all Y which admit a linear continuous surjective mapping T: Cp([1 , α]) → Cp(Y) is given. We also observe that for every countable ordinal α all closed linear subspaces of Cp([1 , α]) are distinguished, thereby answering an open question posed in Ka̧kol and Leiderman (Proc AMS Ser B, 2021).

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

2021

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

115

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

ES - Španělské království

Počet stran výsledku

11

Strana od-do

199

Kód UT WoS článku

000698668600001

EID výsledku v databázi Scopus

2-s2.0-85115337368