Another observation about operator compressions
Probability
2011-02-18 v2 Spectral Theory
Abstract
Let be a self-adjoint operator on a finite dimensional Hilbert space. It is shown that the distribution of the eigenvalues of a compression of to a subspace of a given dimension is almost the same for almost all subspaces. This is a coordinate-free analogue of a recent result of Chatterjee and Ledoux on principal submatrices. The proof is based on measure concentration and entropy techniques, and the result improves on some aspects of the result of Chatterjee and Ledoux.
Cite
@article{arxiv.1001.1954,
title = {Another observation about operator compressions},
author = {Elizabeth S. Meckes and Mark W. Meckes},
journal= {arXiv preprint arXiv:1001.1954},
year = {2011}
}
Comments
6 pages; discussion expanded slightly and minor errors corrected