Another observation about operator compressions

Details Another observation about operator compressions Another observation about operator compressions

2010-01-12

arxiv.org/abs/1001.1954v2

Proc. Amer. Math. Soc. 139 (2011)

Mathematics

Probability

6 pages; discussion expanded slightly and minor errors corrected

Scientific paper

Let $T$ be a self-adjoint operator on a finite dimensional Hilbert space. It is shown that the distribution of the eigenvalues of a compression of $T$ 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.

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