Spectral dominance and commuting chains

Hoai, Bich; Johnson, Charles; Spitkovsky, Ilya

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

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 $A$ “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.

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