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ZOO OF IDEAL SCHAUDER BASES

Part of: Normed linear spaces and Banach spaces; Banach lattices Generalities Set theory

Published online by Cambridge University Press:  05 September 2025

ADAM KWELA Open the ORCID record for ADAM KWELA [Opens in a new window]  and
JAROSŁAW SWACZYNA Open the ORCID record for JAROSŁAW SWACZYNA [Opens in a new window]
ADAM KWELA*
Affiliation:
INSTITUTE OF MATHEMATICS FACULTY OF MATHEMATICS PHYSICS AND INFORMATICS UNIVERSITY OF GDAŃSK UL. WITA STWOSZA 57 80-308 GDAŃSK POLAND URL: https://mat.ug.edu.pl/~akwela
JAROSŁAW SWACZYNA
Affiliation:
INSTITUTE OF MATHEMATICS ŁÓDŹ UNIVERSITY OF TECHNOLOGY ALEJE POLITECHNIKI 8 93-590 ŁÓDŹ POLAND E-mail: jaroslaw.swaczyna@p.lodz.pl
*
E-mail: Adam.Kwela@ug.edu.pl
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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.

Keywords

filter bases in Banach spacesideal bases in Banach spacesgeneralised basesBorel and analytic idealsideal convergence of series

MSC classification

Primary: 46B15: Summability and bases 03E15: Descriptive set theory 03E75: Applications of set theory
Secondary: 46B20: Geometry and structure of normed linear spaces 54A20: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)

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Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 31
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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