Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces

Autor:	Kania, Tomasz, Swaczyna, Jarosław
Rok vydání:	2020
Předmět:	Mathematics - Functional Analysis Mathematics - Logic Primary 46B20 46H40 Secondary 03E55 03E60
Druh dokumentu:	Working Paper
DOI:	10.1112/blms.12415
Popis:	Assuming the existence of certain large cardinal numbers, we prove that for every projective filter $\mathscr F$ over the set of natural numbers, $\mathscr{F}$-bases in Banach spaces have continuous coordinate functionals. In particular, this applies to the filter of statistical convergence, thereby we solve a problem by V. Kadets (at least under the presence of certain large cardinals). In this setting, we recover also a result of Kochanek who proved continuity of coordinate functionals for countably generated filters (Studia Math., 2012). Comment: 10 pp
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2005.04873 Zobrazit plný text záznamu View this record from Arxiv