Publication: Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞
Date
2021
Authors
Ansorena, José L.
Director
Publisher
Wiley
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa
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 unconditional basis up to permutation.
Description
Keywords
Unconditional basis, Quasi-Banach space, L-p-spaces
Department
Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika
Faculty/School
Degree
Doctorate program
item.page.cita
Ansorena, J.L and Albiac, F, 'Projections and unconditional bases in direct sums of ℓp spaces, 0<p≤∞', Nov. 30 2021, Mathematische Nachrichten, doi: 10.1002/mana.201900537
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