Continuity of coordinate functionals of filter bases in Banach spaces

0569855 - MÚ 2024 RIV US eng J - Článek v odborném periodiku
de Rancourt, N. - Kania, Tomasz - Swaczyna, Jarosław
Continuity of coordinate functionals of filter bases in Banach spaces.
Journal of Functional Analysis. Roč. 284, č. 9 (2023), č. článku 109869. ISSN 0022-1236. E-ISSN 1096-0783
Grant CEP: GA ČR(CZ) GJ19-07129Y
Institucionální podpora: RVO:67985840
Klíčová slova: automatic continuity * definable filters * filter bases in Banach spaces * generalised bases
Obor OECD: Pure mathematics
Impakt faktor: 1.7, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.jfa.2023.109869

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.
Trvalý link: https://hdl.handle.net/11104/0341192