Continuity of coordinate functionals of filter bases in Banach spaces

De Rancourt, Noé; Kania, Tomasz; Swaczyna, Jarosław

Type de document :

Compte-rendu et recension critique d'ouvrage

DOI :

10.1016/j.jfa.2023.109869

Titre :

Continuity of coordinate functionals of filter bases in Banach spaces

Auteur(s) :

De Rancourt, Noé [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Univerzita Karlova [Praha, Česká republika] = Charles University [Prague, Czech Republic] [UK]
Kania, Tomasz [Auteur]
Faculty of Mathematics and Computer Science of the Jagiellonian University
Institute of Mathematics of the Czech Academy of Science [IM / CAS]
Swaczyna, Jarosław [Auteur]
Institute of Mathematics of the Czech Academy of Science [IM / CAS]
Łódź University of Technology

Titre de la revue :

Journal of Functional Analysis

Pagination :

109869

Éditeur :

Elsevier

Date de publication :

2023-05

ISSN :

0022-1236

Mot(s)-clé(s) en anglais :

Filter bases in Banach spaces
Generalised bases
Automatic continuity
Definable filters

Discipline(s) HAL :

Mathématiques [math]/Analyse fonctionnelle [math.FA]

Résumé en anglais : [en]

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 ...
Lire la suite >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 ([Bull. Lond. Math. Soc. 53 (2021)]) 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.Lire moins >

Langue :

Anglais

Vulgarisation :

Non

Collections :