Analytic P-ideals and Banach spaces

We study the interplay between Banach space theory and theory of analytic P-ideals. Applying the observation that, up to isomorphism, all Banach spaces with unconditional bases can be constructed in a way very similar to the construction of analytic P-ideals from submeasures, we point out numerous s...

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Bibliographic Details
Published in:Journal of functional analysis 2020-11, Vol.279 (8), p.108702, Article 108702
Main Authors: Borodulin-Nadzieja, Piotr, Farkas, Barnabás
Format: Article
Language:English
Subjects:
Analytic P-ideals
Boundedly complete bases
Extended norms
Families of finite sets
Non-pathological submeasures
Schreier spaces
Shrinking bases
Unconditional Schauder bases
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Summary:We study the interplay between Banach space theory and theory of analytic P-ideals. Applying the observation that, up to isomorphism, all Banach spaces with unconditional bases can be constructed in a way very similar to the construction of analytic P-ideals from submeasures, we point out numerous symmetries between the two theories. Also, we investigate a special case, the interactions between combinatorics of families of finite sets, topological properties of the “Schreier type” Banach spaces associated to these families, and the complexity of ideals generated by the canonical bases in these spaces. Among other results, we present some new examples of Banach spaces and analytic P-ideals, a new characterization of precompact families and its applications to enhance Pták's Lemma and Mazur's Lemma.
ISSN:0022-1236
1096-0783
DOI:10.1016/j.jfa.2020.108702