Characterization of atomic decompositions, Banach frames, Xd-frames, duals and synthesis-pseudo-duals, with application to Hilbert frame theory

Details Characterization of atomic decompositions, Banach frames, Xd-frames, duals and synthesis-pseudo-duals, with application to Hilbert frame theory Characterization of atomic decompositions, Banach frames, Xd-frames, duals and synthesis-pseudo-duals, with application to Hilbert frame theory

2011-08-31

arxiv.org/abs/1108.6282v1

Mathematics

Functional Analysis

Scientific paper

In this paper we give a characterization of atomic decompositions, Banach frames, $X_d$-Riesz bases, $X_d$-frames, $X_d$-Bessel sequences, sequences satisfying the lower $X_d$-frame condition, duals of $X_d$-frames and synthesis pseudo-duals, based on an operator acting on the canonical basis of a sequence space. We discuss expansions in $X$ and $X^*$. Further, we consider necessary and sufficient conditions on operators to preserve the sequence type of the listed concepts. As a consequence, we solve some problems in Hilbert frame theory.

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