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Abstract:

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.

Registro:

Documento: Artículo
Título:Duality, reflexivity and atomic decompositions in Banach spaces
Autor:Carando, D.; Lassalle, S.
Filiación:Departamento de Matematica - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina
Palabras clave:Atomic decompositions; Banach frames; Duality; Reflexivity
Año:2009
Volumen:191
Número:1
Página de inicio:67
Página de fin:80
DOI: http://dx.doi.org/10.4064/sm191-1-5
Título revista:Studia Mathematica
Título revista abreviado:Stud. Math.
ISSN:00393223
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393223_v191_n1_p67_Carando

Referencias:

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Citas:

---------- APA ----------
Carando, D. & Lassalle, S. (2009) . Duality, reflexivity and atomic decompositions in Banach spaces. Studia Mathematica, 191(1), 67-80.
http://dx.doi.org/10.4064/sm191-1-5
---------- CHICAGO ----------
Carando, D., Lassalle, S. "Duality, reflexivity and atomic decompositions in Banach spaces" . Studia Mathematica 191, no. 1 (2009) : 67-80.
http://dx.doi.org/10.4064/sm191-1-5
---------- MLA ----------
Carando, D., Lassalle, S. "Duality, reflexivity and atomic decompositions in Banach spaces" . Studia Mathematica, vol. 191, no. 1, 2009, pp. 67-80.
http://dx.doi.org/10.4064/sm191-1-5
---------- VANCOUVER ----------
Carando, D., Lassalle, S. Duality, reflexivity and atomic decompositions in Banach spaces. Stud. Math. 2009;191(1):67-80.
http://dx.doi.org/10.4064/sm191-1-5