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ZOO OF IDEAL SCHAUDER BASES

Published online by Cambridge University Press:  05 September 2025

ADAM KWELA*
Affiliation:
INSTITUTE OF MATHEMATICS FACULTY OF MATHEMATICS PHYSICS AND INFORMATICS https://ror.org/011dv8m48 UNIVERSITY OF GDAŃSK UL. WITA STWOSZA 57 80-308 GDAŃSK POLAND URL: https://mat.ug.edu.pl/~akwela
JAROSŁAW SWACZYNA
Affiliation:
INSTITUTE OF MATHEMATICS https://ror.org/00s8fpf52 ŁÓDŹ UNIVERSITY OF TECHNOLOGY ALEJE POLITECHNIKI 8 93-590 ŁÓDŹ POLAND E-mail: jaroslaw.swaczyna@p.lodz.pl

Abstract

We investigate the notion of ideal (equivalently: filter) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones, especially within classical Banach spaces ($\ell _p$, $c_0$, and James’ space). Those examples lead to distinguishing and characterizing ideals (equivalently: filters) in terms of Schauder bases. We investigate the relationship between possibly basic sequences and ideals (equivalently: filters) on the set of natural numbers.

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Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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