Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations

Details Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations

1998-11-24

arxiv.org/abs/math/9811148v1

Mathematics

Functional Analysis

to appear: J. of Fourier Anal. and Appl's

Scientific paper

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. A result of N.J. Kalton is included which shows that this is best possible in that: 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 normalized tight frames or as a sum of an orthonormal basis and a Riesz basis for H. Finally, every frame can be represented as a (multiple of a) average of two orthonormal bases for a larger Hilbert space.

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