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Tight-minimal dichotomies in Banach spaces

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Author(s):
Caceres-Rigo, Alejandra C. ; Ferenczi, Valentin
Total Authors: 2
Document type: Journal article
Source: STUDIA MATHEMATICA; v. N/A, p. 47-pg., 2025-04-06.
Abstract

We extend the methods used by V. Ferenczi and Ch. Rosendal to obtain the "third dichotomy" in the program of classification of Banach spaces up to subspaces, in order to prove that a Banach space E with an admissible system of blocks (DE, AE) contains an infinite-dimensional subspace with a basis which is either AE-tight or AEminimal. In this setting we obtain, in particular, dichotomies regarding subsequences of a basis, and as a corollary, we show that every normalized basic sequence (en)n has a subsequence which satisfies a tightness property or is spreading. Other dichotomies between notions of minimality and tightness are demonstrated, and the Ferenczi-Godefroy interpretation of tightness in terms of Baire category is extended to this new context. (AU)

FAPESP's process: 17/18976-5 - Study of the borelian complexity of certain properties of Banach spaces
Grantee:Alejandra Carolina Cáceres Rigo
Support Opportunities: Scholarships in Brazil - Doctorate
FAPESP's process: 16/25574-8 - Geometry of Banach Spaces
Grantee:Valentin Raphael Henri Ferenczi
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 22/04745-0 - Envelopes and ultrahomogeneity in Banach spaces
Grantee:Valentin Raphael Henri Ferenczi
Support Opportunities: Scholarships abroad - Research
FAPESP's process: 23/12916-1 - Geometry of Banach spaces
Grantee:Valentin Raphael Henri Ferenczi
Support Opportunities: Research Projects - Thematic Grants