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Summer 1999 Local theory of frames and schauder bases for Hilbert space
Peter G. Casazza
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Illinois J. Math. 43(2): 291-306 (Summer 1999). DOI: 10.1215/ijm/1255985216


We develope a local theory for frames on finite-dimensional Hilbert spaces. We show that for every frame. $(f_{i})^{m}_{i=1}$ for an $n$-dimensional Hilbert space, and for every $\epsilon \gt 0$, there is a subset $I \subset {1,2,\ldots,m}$ with $|I| \geq (1-\epsilon)n$ so that $(f_{i})_{i \in I}$ is a Riesz basis for its span with Riesz basis constant a function of $\epsilon$, the frame bounds, and $(||f_{i}||)^{m}_{i=1}$, but independent of m and n. We also construct an example of a normalized frame for a Hilbert space $H$ which contains a subset which forms a Schauder basis for $H$, but contains no subset which is a Riesz basis for $H$. We give examples to show that all of our results are best possible, and that all parameters are necessary.


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Peter G. Casazza. "Local theory of frames and schauder bases for Hilbert space." Illinois J. Math. 43 (2) 291 - 306, Summer 1999.


Published: Summer 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0934.46009
MathSciNet: MR1703189
Digital Object Identifier: 10.1215/ijm/1255985216

Primary: 46C05
Secondary: 42C15 , 46B15

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 2 • Summer 1999
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