Every frame is a sum of three (but not two) orthonormal bases—and other frame representations |
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Authors: | Peter G Casazza |
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Institution: | (1) Department of Mathematics, The University of Missouri, 65211 Columbia, Missouri |
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Abstract: | We show that every frame for a Hilbert space H can be written as a (multiple of a) sum of three orthonormal bases for H. We
next show that this result is best possible by including a result of Kalton: A frame can be represented as a linear combination
of two orthonormal bases if and only if it is a Riesz basis. We further show that every frame can be written as a (multiple
of a) sum of two tight frames with frame bounds one or a sum of an orthonormal basis and a Riesz basis for H. Finally, every
frame can be written as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.
Acknowledgements and Notes. This research was supported by NSF DMS 9701234. Part of this research was conducted while the author was a visitor at the
“Workshop on Linear Analysis and Probability”, Texas A&M University. |
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Keywords: | 46C05 47A05 47B65 |
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