Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞
Date
2021
Version
Acceso abierto / Sarbide irekia
Type
Artículo / Artikulua
Version
Versión aceptada / Onetsi den bertsioa
Project Identifier
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095366-B-I00/ES/ 
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/
AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107701GB-I00/ES/
Impact
Abstract
We show that every unconditional basis in a finite direct sum ⊕p∈Aℓp , with A ⊂ (0,∞], splits into unconditional bases of each summand. This settles a 40 years old question raised in 'A. Ortyński, Unconditional bases in ℓp ⊕ ℓq, 0< p < q <1, Math. Nachr. 103 (1981), 109–116'. As an application we obtain that for any A ⊂ (0,1] finite, the spaces Z = ⊕p∈A ℓp,Z ⊕ ℓ2, and Z ⊕ c0 have a unique uncondi ...
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Subject
Unconditional basis,
Quasi-Banach space,
L-p-spaces
Publisher
Wiley
Published in
Mathematische Nachrichten, 294 (11), pp. 2052-2062, 2021
Departament
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Publisher version
Sponsorship
Both authors were supported by the Spanish Ministry for Science, Innovation, and Universities, Grant PGC2018-095366-B-I00 for ‘Análisis Vectorial, Multilineal y Approximación’. The first-named author also acknowledges the support from the Spanish Ministry for Science and Innovation, Grant PID2019-107701GB-I00 for ‘Operators, Lattices, and Structure of Banach spaces.
