Continuity of coordinate functionals of filter bases in Banach spaces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00569855" target="_blank" >RIV/67985840:_____/23:00569855 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.jfa.2023.109869" target="_blank" >https://doi.org/10.1016/j.jfa.2023.109869</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jfa.2023.109869" target="_blank" >10.1016/j.jfa.2023.109869</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Continuity of coordinate functionals of filter bases in Banach spaces

Popis výsledku v původním jazyce

We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors (Kania and Swaczyna, 2021 [9]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyond the projective class remains a mystery, we prove that a basis with respect to an arbitrary filter that has continuous coordinate functionals is also a basis with respect to a filter that is analytic.

Název v anglickém jazyce

Continuity of coordinate functionals of filter bases in Banach spaces

Popis výsledku anglicky

We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal hypothesis from the result established by the two last-named authors (Kania and Swaczyna, 2021 [9]) at the expense of reducing the generality from projective to analytic. In particular, we obtain a ZFC solution to Kadets' problem of continuity of coordinate functionals associated with bases with respect to the filter of statistical convergence. Even though the automatic continuity of coordinate functionals beyond the projective class remains a mystery, we prove that a basis with respect to an arbitrary filter that has continuous coordinate functionals is also a basis with respect to a filter that is analytic.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Metody lineární analýzy v operátorových algebrách a naopak</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

Journal of Functional Analysis

ISSN

0022-1236

e-ISSN

1096-0783

Svazek periodika

284

Číslo periodika v rámci svazku

9

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

109869

Kód UT WoS článku

000944346100001

EID výsledku v databázi Scopus

2-s2.0-85148346532