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...

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Autores principales: Carando, Daniel German, Lassalle, Silvia Beatriz
Publicado: 2009
Materias:
Atomic decompositions
Banach frames
Duality
Reflexivity
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v191_n1_p67_Carando
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 paper:paper_00393223_v191_n1_p67_Carando
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spelling paper:paper_00393223_v191_n1_p67_Carando2023-06-08T15:03:32Z Duality, reflexivity and atomic decompositions in Banach spaces Carando, Daniel German Lassalle, Silvia Beatriz 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. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v191_n1_p67_Carando 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, Daniel German
Lassalle, Silvia Beatriz
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.
author Carando, Daniel German
Lassalle, Silvia Beatriz
author_facet Carando, Daniel German
Lassalle, Silvia Beatriz
author_sort Carando, Daniel German
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
publishDate 2009
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v191_n1_p67_Carando
http://hdl.handle.net/20.500.12110/paper_00393223_v191_n1_p67_Carando
work_keys_str_mv AT carandodanielgerman dualityreflexivityandatomicdecompositionsinbanachspaces
AT lassallesilviabeatriz dualityreflexivityandatomicdecompositionsinbanachspaces
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