A type (4) space in (FR)-classification
Spiros A. Argyros, Antonis Manoussakis, Anna Pelczar-Barwacz

TL;DR
This paper constructs a reflexive Banach space with an unconditional basis that is quasi-minimal and tight by range, fitting into the type (4) classification in Gowers' program, extending the understanding of Banach space structures.
Contribution
It introduces a new unconditional variant of the Gowers Hereditarily Indecomposable space, classified as type (4) in Ferenczi-Rosendal's list, within Gowers' classification framework.
Findings
The space is reflexive with an unconditional basis.
It is quasi-minimal and tight by range.
It extends the class of known Banach spaces with these properties.
Abstract
We present a reflexive Banach space with an unconditional basis which is quasi-minimal and tight by range, i.e. of type (4) in Ferenczi-Rosendal list within the framework of Gowers' classification program of Banach spaces. The space is an unconditional variant of the Gowers Hereditarily Indecomposable space with asymptotically unconditional basis.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Advanced Topics in Algebra
