Another observation about operator compressions
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- by Elizabeth S. Meckes and Mark W. Meckes PDF
- Proc. Amer. Math. Soc. 139 (2011), 1433-1439 Request permission
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.References
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Additional Information
- Elizabeth S. Meckes
- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
- MR Author ID: 754850
- Email: elizabeth.meckes@case.edu
- Mark W. Meckes
- Affiliation: Department of Mathematics, Case Western Reserve University, Cleveland, Ohio 44106
- MR Author ID: 729101
- Email: mark.meckes@case.edu
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1433-1439
- MSC (2010): Primary 47A20, 60E15, 60B20
- DOI: https://doi.org/10.1090/S0002-9939-2010-10671-8
- MathSciNet review: 2748436