Duality, reflexivity and atomic decompositions in Banach spaces

We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Carando, D., Lassalle, S.
Formato: JOUR
Materias:
Atomic decompositions
Banach frames
Duality
Reflexivity
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00393223_v191_n1_p67_Carando
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00393223_v191_n1_p67_Carando
record_format dspace
spelling todo:paper_00393223_v191_n1_p67_Carando2023-10-03T14:49:45Z Duality, reflexivity and atomic decompositions in Banach spaces Carando, D. Lassalle, S. Atomic decompositions Banach frames Duality Reflexivity We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions. © PInstytut Matematyczny PAN, 2009. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00393223_v191_n1_p67_Carando
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Atomic decompositions
Banach frames
Duality
Reflexivity
spellingShingle Atomic decompositions
Banach frames
Duality
Reflexivity
Carando, D.
Lassalle, S.
Duality, reflexivity and atomic decompositions in Banach spaces
topic_facet Atomic decompositions
Banach frames
Duality
Reflexivity
description We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions. © PInstytut Matematyczny PAN, 2009.
format JOUR
author Carando, D.
Lassalle, S.
author_facet Carando, D.
Lassalle, S.
author_sort Carando, D.
title Duality, reflexivity and atomic decompositions in Banach spaces
title_short Duality, reflexivity and atomic decompositions in Banach spaces
title_full Duality, reflexivity and atomic decompositions in Banach spaces
title_fullStr Duality, reflexivity and atomic decompositions in Banach spaces
title_full_unstemmed Duality, reflexivity and atomic decompositions in Banach spaces
title_sort duality, reflexivity and atomic decompositions in banach spaces
url http://hdl.handle.net/20.500.12110/paper_00393223_v191_n1_p67_Carando
work_keys_str_mv AT carandod dualityreflexivityandatomicdecompositionsinbanachspaces
AT lassalles dualityreflexivityandatomicdecompositionsinbanachspaces
_version_ 1782023684414767104

Ejemplares similares