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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Another observation about operator compressions


Authors: Elizabeth S. Meckes and Mark W. Meckes
Journal: Proc. Amer. Math. Soc. 139 (2011), 1433-1439
MSC (2010): Primary 47A20, 60E15, 60B20
Published electronically: September 2, 2010
MathSciNet review: 2748436
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Abstract: 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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Additional Information

Elizabeth S. Meckes
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Email: elizabeth.meckes@case.edu

Mark W. Meckes
Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
Email: mark.meckes@case.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10671-8
PII: S 0002-9939(2010)10671-8
Received by editor(s): January 12, 2010
Received by editor(s) in revised form: April 29, 2010
Published electronically: September 2, 2010
Additional Notes: The first author’s research was supported by an American Institute of Mathematics Five-Year Fellowship and NSF grant DMS-0852898.
The second author’s research was supported by NSF grant DMS-0902203.
Communicated by: Marius Junge
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.