Projections and unconditional bases in direct sums of ℓp SPACES, 0<p≤∞
Fecha
2021Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
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10.1002/mana.201900537
Resumen
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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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. [--]
Materias
Unconditional basis,
Quasi-Banach space,
L-p-spaces
Editor
Wiley
Publicado en
Mathematische Nachrichten, 294 (11), pp. 2052-2062, 2021
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
Versión del editor
Entidades Financiadoras
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.