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Abstract: Let $T$ be a self-adjoint operator on a finite dimensional Hilbert space. Itis shown that the distribution of the eigenvalues of a compression of $T$ to asubspace of a given dimension is almost the same for almost all subspaces. Thisis a coordinate-free analogue of a recent result of Chatterjee and Ledoux onprincipal submatrices. The proof is based on measure concentration and entropytechniques, and the result improves on some aspects of the result of Chatterjeeand Ledoux.



Author: Elizabeth S. Meckes, Mark W. Meckes

Source: https://arxiv.org/







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