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Abstract:

We study conditions on a Banach frame that ensures the validity of a reconstruction formula. In particular, we show that any Banach frames for (a subspace of) Lp or Lp,q (1≤;p<∞) with respect to a solid sequence space always satisfies an unconditional reconstruction formula. The existence of reconstruction formulas allows us to prove some James-type results for atomic decompositions: an unconditional atomic decomposition (or unconditional Schauder frame) for X is shrinking (respectively, boundedly complete) if and only if X does not contain an isomorphic copy of ℓ1 (respectively, c0). © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:The reconstruction formula for Banach frames and duality
Autor:Carando, D.; Lassalle, S.; Schmidberg, P.
Filiación:Departamento de Matemática - 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:2011
Volumen:163
Número:5
Página de inicio:640
Página de fin:651
DOI: http://dx.doi.org/10.1016/j.jat.2011.02.007
Título revista:Journal of Approximation Theory
Título revista abreviado:J. Approx. Theory
ISSN:00219045
CODEN:JAXTA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00219045_v163_n5_p640_Carando

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Citas:

---------- APA ----------
Carando, D., Lassalle, S. & Schmidberg, P. (2011) . The reconstruction formula for Banach frames and duality. Journal of Approximation Theory, 163(5), 640-651.
http://dx.doi.org/10.1016/j.jat.2011.02.007
---------- CHICAGO ----------
Carando, D., Lassalle, S., Schmidberg, P. "The reconstruction formula for Banach frames and duality" . Journal of Approximation Theory 163, no. 5 (2011) : 640-651.
http://dx.doi.org/10.1016/j.jat.2011.02.007
---------- MLA ----------
Carando, D., Lassalle, S., Schmidberg, P. "The reconstruction formula for Banach frames and duality" . Journal of Approximation Theory, vol. 163, no. 5, 2011, pp. 640-651.
http://dx.doi.org/10.1016/j.jat.2011.02.007
---------- VANCOUVER ----------
Carando, D., Lassalle, S., Schmidberg, P. The reconstruction formula for Banach frames and duality. J. Approx. Theory. 2011;163(5):640-651.
http://dx.doi.org/10.1016/j.jat.2011.02.007