Publication:
Uniqueness of unconditional basis of ℓ2⊕T(2)

Date

2022

Authors

Director

Publisher

American Mathematical Society
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa

Project identifier

AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/recolecta
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/recolecta
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Abstract

We provide a new extension of Pitt’s theorem for compact operators between quasi-Banach lattices which permits to describe unconditional bases of finite direct sums of Banach spaces X1 · · · Xn as direct sums of unconditional bases of their summands. The general splitting principle we obtain yields, in particular, that if each Xi has a unique unconditional basis (up to equivalence and permutation), then X1 · · · Xn has a unique unconditional basis too. Among the novel applications of our techniques to the structure of Banach and quasi-Banach spaces we have that the space ℓ2⊕T(2) has a unique unconditional basis.

Description

Keywords

Banach lattice, Equivalence of bases, Hardy spaces, Quasi-Banach space, Tsirelson space, Unconditional basis, Uniqueness of structure

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika

Faculty/School

Degree

Doctorate program

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