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Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces by Kania, Tomasz; Swaczyna, Jarosław is a scholarly article available to read on EtoBox.

What is Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces about?

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).

Author

Kania, Tomasz; Swaczyna, Jarosław

Published

2020

Language

EN