The reconstruction formula for Banach frames and duality
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 reco...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00219045_v163_n5_p640_Carando |
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todo:paper_00219045_v163_n5_p640_Carando2023-10-03T14:22:37Z The reconstruction formula for Banach frames and duality Carando, D. Lassalle, S. Schmidberg, P. Atomic decompositions Banach frames Duality Reflexivity 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. 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_00219045_v163_n5_p640_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. Schmidberg, P. The reconstruction formula for Banach frames and duality |
| topic_facet |
Atomic decompositions Banach frames Duality Reflexivity |
| description |
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. |
| format |
JOUR |
| author |
Carando, D. Lassalle, S. Schmidberg, P. |
| author_facet |
Carando, D. Lassalle, S. Schmidberg, P. |
| author_sort |
Carando, D. |
| title |
The reconstruction formula for Banach frames and duality |
| title_short |
The reconstruction formula for Banach frames and duality |
| title_full |
The reconstruction formula for Banach frames and duality |
| title_fullStr |
The reconstruction formula for Banach frames and duality |
| title_full_unstemmed |
The reconstruction formula for Banach frames and duality |
| title_sort |
reconstruction formula for banach frames and duality |
| url |
http://hdl.handle.net/20.500.12110/paper_00219045_v163_n5_p640_Carando |
| work_keys_str_mv |
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| _version_ |
1807323931792637952 |