Upper and lower estimates for schauder frames and atomic decompositions
Functional Analysis
2012-02-14 v1
Abstract
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.
Cite
@article{arxiv.1202.2492,
title = {Upper and lower estimates for schauder frames and atomic decompositions},
author = {Kevin Beanland and Daniel Freeman and Rui Liu},
journal= {arXiv preprint arXiv:1202.2492},
year = {2012}
}
Comments
22 pages