Spectral dominance and commuting chains

Bich T. Hoai; Charles R. Johnson; Ilya M. Spitkovsky

doi:10.1090/S0002-9939-08-09104-1

Spectral dominance and commuting chains

Bich T. Hoai, Charles R. Johnson, Ilya M. Spitkovsky

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

A positive semidefinite (PSD) operator A "spectrally dominates" 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.

Original language	English (US)
Pages (from-to)	2019-2029
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-08-09104-1
State	Published - Jun 2008

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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AB - A positive semidefinite (PSD) operator A "spectrally dominates" a PSD operator B if At - Bt 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.

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Spectral dominance and commuting chains

Abstract

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