Uniqueness of unconditional basis of Hp(T) ⊕ 2 and Hp(T) ⊕ T (2) for 0 < p < 1
Fecha
2022Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión publicada / Argitaratu den bertsioa
Identificador del proyecto
Impacto
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10.1016/j.jfa.2022.109597
Resumen
Our goal in this paper is to advance the state of the art of
the topic of uniqueness of unconditional basis. To that end
we establish general conditions on a pair (X, Y) formed by a
quasi-Banach space X and a Banach space Y which guarantee that every unconditional basis of their direct sum X ⊕ Y
splits into unconditional bases of each summand. As application of our methods we obtain that, amo ...
[++]
Our goal in this paper is to advance the state of the art of
the topic of uniqueness of unconditional basis. To that end
we establish general conditions on a pair (X, Y) formed by a
quasi-Banach space X and a Banach space Y which guarantee that every unconditional basis of their direct sum X ⊕ Y
splits into unconditional bases of each summand. As application of our methods we obtain that, among others, the spaces
Hp(Td) ⊕ T (2) and Hp(Td) ⊕ 2, for p ∈ (0, 1) and d ∈ N,
have a unique unconditional basis (up to equivalence and permutation). [--]
Materias
Hardy spaces,
Lattice techniques in quasi-Banach spaces,
Tsirelson space,
Uniqueness of unconditional basis
Editor
Elsevier
Publicado en
Journal of Functional Analysis 283 (2022) 109597
Departamento
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas /
Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
F. Albiac acknowledges the support of the Spanish Ministry for Science and Innovation under Grant PID2019-107701GB-I00 for Operators, lattices, and structure of Banach spaces. F. Albiac and J. L. Ansorena acknowledge the support of the Spanish Ministry for Science, Innovation, and Universities under Grant PGC2018-095366-B-I00 for Análisis Vectorial, Multilineal y Aproximación. P. Wojtaszczyk was supported by National Science Centre, Poland grant UMO-2016/21/B/ST1/00241.