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Local theory of frames and Schauder bases for Hilbert space

Peter G. Casazza
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Abstract

We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of the space. We also construct a normalized frame for a Hilbert space which contains a subset which is a Schauder basis for H but does not contain any subset which is a Riesz basis for H.

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Peter G. Casazza. 1998-11-24. Local theory of frames and Schauder bases for Hilbert space. https://arxiv.org/abs/math/9811147

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