Upper and lower estimates for schauder frames and atomic decompositions

Details Upper and lower estimates for schauder frames and atomic decompositions Upper and lower estimates for schauder frames and atomic decompositions

2012-02-12

arxiv.org/abs/1202.2492v1

Mathematics

Functional Analysis

22 pages

Scientific paper

We prove that a Schauder frame for any separable Banach space is shrinking if and only if it has an associated space with a shrinking basis, and that a Schauder frame for any separable Banach space is shrinking and boundedly complete if and only if it has a reflexive associated space. To obtain these results, we prove that the upper and lower estimate theorems for finite dimensional decompositions of Banach spaces can be extended and modified to Schauder frames. We show as well that if a separable infinite dimensional Banach space has a Schauder frame, then it also has a Schauder frame which is not shrinking.

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