The reconstruction formula for Banach frames and duality |
| |
Authors: | Daniel Carando Silvia Lassalle Pablo Schmidberg |
| |
Affiliation: | Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, (1428) Buenos Aires, Argentina |
| |
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) or () 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 is shrinking (respectively, boundedly complete) if and only if does not contain an isomorphic copy of (respectively, ). |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|