Expansion of approximate Bessel sequences to approximate Schauder frames for Banach spaces

2021/02/05 by K. Mahesh Krishna, Krishna, K. Mahesh, P. Sam Johnson +1
Mathematics · Engineering · #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2102.03288

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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