Efimov spaces and the separable quotient problem for spaces C-P(K)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00480123" target="_blank" >RIV/67985840:_____/18:00480123 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.08.010" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2017.08.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2017.08.010" target="_blank" >10.1016/j.jmaa.2017.08.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Efimov spaces and the separable quotient problem for spaces C-P(K)

Popis výsledku v původním jazyce

The classic Rosenthal-Lacey theorem asserts that the Banach space C(K)of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or ...2. More recently, Kakol and Saxon [20] proved that the space Cp(K) endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence Cp(betaN) lacks infinite-dimensional separable quotient algebras. This motivates the following question: (...) Does Cp(K) admit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does Cp(betaN) admit SQ? Our main theorem implies that Cp(K) has SQ for any compact space K containing a copy of betaN. Consequently, this result reduces problem (...) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of betaN).

Název v anglickém jazyce

Efimov spaces and the separable quotient problem for spaces C-P(K)

Popis výsledku anglicky

The classic Rosenthal-Lacey theorem asserts that the Banach space C(K)of continuous real-valued maps on an infinite compact space K has a quotient isomorphic to c or ...2. More recently, Kakol and Saxon [20] proved that the space Cp(K) endowed with the pointwise topology has an infinite-dimensional separable quotient algebra iff K has an infinite countable closed subset. Hence Cp(betaN) lacks infinite-dimensional separable quotient algebras. This motivates the following question: (...) Does Cp(K) admit an infinite-dimensional separable quotient (shortly SQ) for any infinite compact space K? Particularly, does Cp(betaN) admit SQ? Our main theorem implies that Cp(K) has SQ for any compact space K containing a copy of betaN. Consequently, this result reduces problem (...) to the case when K is an Efimov space (i.e. K is an infinite compact space that contains neither a non-trivial convergent sequence nor a copy of betaN).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF16-34860L" target="_blank" >GF16-34860L: Logika a topologie v Banachových prostorech</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

457

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

104-113

Kód UT WoS článku

000412152100007

EID výsledku v databázi Scopus

2-s2.0-85027490226