Tight projections of frames on infinite dimensional Hilbert spaces
Functional Analysis
2012-11-15 v1
Abstract
We characterize the frames on an infinite dimensional separable Hilbert space that can be projected to a tight frame for an infinite dimensional subspace. A result of Casazza and Leon states that an arbitrary frame for a 2N- or (2N-1)-dimensional Hilbert space can be projected to a tight frame for an N-dimensional subspace. Surprisingly, we demonstrate a large class of frames for infinite dimensional Hilbert spaces which cannot be projected to a tight frame for any infinite dimensional subspace.
Cite
@article{arxiv.1211.3360,
title = {Tight projections of frames on infinite dimensional Hilbert spaces},
author = {John Jasper},
journal= {arXiv preprint arXiv:1211.3360},
year = {2012}
}