Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces
Functional Analysis
2021-02-08 v1
Abstract
It is known in Hilbert space frame theory that a Bessel sequence can be expanded to a frame. Contrary to Hilbert space situation, using a result of Casazza and Christensen, we show that there are Banach spaces and approximate Bessel sequences which can not be expanded to approximate Schauder frames. We characterize Banach spaces in which one can expand approximate Bessel sequences to approximate Schauder frames.
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Cite
@article{arxiv.2102.03288,
title = {Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces},
author = {K. Mahesh Krishna and P. Sam Johnson},
journal= {arXiv preprint arXiv:2102.03288},
year = {2021}
}
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5 pages