Spectral dominance and commuting chains
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- by Bich T. Hoai, Charles R. Johnson and Ilya M. Spitkovsky PDF
- Proc. Amer. Math. Soc. 136 (2008), 2019-2029 Request permission
Abstract:
A positive semidefinite (PSD) operator $A$ βspectrally dominatesβ a PSD operator $B$ if $A^t-B^t$ is PSD for all $t>0$. We (i) give a new characterization of spectral dominance in finite dimensions in terms of a monotonic chain of intermediate, pairwise commuting operators and (ii) determine for which pairs $A,B$ spectral dominance persists under the taking of arbitrary compressions. Earlier results about spectral dominance are proven (in finite dimensions) in new ways, and several corollary observations are made.References
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Additional Information
- Bich T. Hoai
- Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185
- Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1043
- Email: bhoai@umich.edu
- Charles R. Johnson
- Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185
- Email: crjohnso@math.wm.edu
- Ilya M. Spitkovsky
- Affiliation: Department of Mathematics, College of William & Mary, Williamsburg, Virginia 23185
- MR Author ID: 191035
- ORCID: 0000-0002-1411-3036
- Email: ilya@math.wm.edu
- Received by editor(s): November 30, 2006
- Received by editor(s) in revised form: January 3, 2007
- Published electronically: February 14, 2008
- Additional Notes: The work on this paper in the summer of 2006 was supported in part by the National Science Foundation Grant No. DMS-0353510
The third author (IMS) is also partially supported by the National Science Foundation Grant No. DMS-0456625. - Communicated by: Joseph A. Ball
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 2019-2029
- MSC (2000): Primary 47A63, 15A57, 15A27
- DOI: https://doi.org/10.1090/S0002-9939-08-09104-1
- MathSciNet review: 2383508