Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations
Functional Analysis
2007-05-23 v1
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. 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.
Keywords
Cite
@article{arxiv.math/9811148,
title = {Every frame is a sum of three (but nottwo) orthonormal bases, and other frame representations},
author = {Peter G. Casazza},
journal= {arXiv preprint arXiv:math/9811148},
year = {2007}
}
Comments
to appear: J. of Fourier Anal. and Appl's