Spectral dominance and commuting chains

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

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)2019-2029
Number of pages11
JournalProceedings of the American Mathematical Society
Volume136
Issue number6
DOIs
StatePublished - Jun 2008

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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