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On the complexity of some inevitable classes of separable Banach spaces.

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posted on 2018-02-13, 00:00 authored by BM BRAGA.
In this paper, we study the descriptive complexity of some inevitable classes of Banach spaces. Precisely, as shown in [Go], every Banach space either contains a hereditarily indecomposable subspace or an unconditional basis, and, as shown in [FR], every Banach space either contains a minimal subspace or a continuously tight subspace. In these notes, we study the complexity of those inevitable classes as well as the complexity of containing a subspace in any of those classes.

History

Publisher Statement

This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications. 2015. 431(1): 682-701. DOI: 10.1016/j.jmaa.2015.05.045.

Publisher

Elsevier Inc.

issn

0022-247X

Issue date

2014-10-01

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    Keywords

    Minimal Banach spaces,continuously tight Banach spacesHI spacesdescriptive set theory, treesBanach spaces dichotomies

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