Spectral dominance and commuting chains

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

Research output: Contribution to journalArticle

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 1 2008

Fingerprint

Positive semidefinite
Operator
Monotonic
Pairwise
Corollary
Compression
Arbitrary

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Spectral dominance and commuting chains. / Hoai, Bich T.; Johnson, Charles R.; Spitkovsky, Ilya.

In: Proceedings of the American Mathematical Society, Vol. 136, No. 6, 01.06.2008, p. 2019-2029.

Research output: Contribution to journalArticle

Hoai, Bich T. ; Johnson, Charles R. ; Spitkovsky, Ilya. / Spectral dominance and commuting chains. In: Proceedings of the American Mathematical Society. 2008 ; Vol. 136, No. 6. pp. 2019-2029.
@article{1016a2fbf6664f959532fe1d305e8115,
title = "Spectral dominance and commuting chains",
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.",
author = "Hoai, {Bich T.} and Johnson, {Charles R.} and Ilya Spitkovsky",
year = "2008",
month = "6",
day = "1",
doi = "10.1090/S0002-9939-08-09104-1",
language = "English (US)",
volume = "136",
pages = "2019--2029",
journal = "Proceedings of the American Mathematical Society",
issn = "0002-9939",
publisher = "American Mathematical Society",
number = "6",

}

TY - JOUR

T1 - Spectral dominance and commuting chains

AU - Hoai, Bich T.

AU - Johnson, Charles R.

AU - Spitkovsky, Ilya

PY - 2008/6/1

Y1 - 2008/6/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=77950635640&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77950635640&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09104-1

DO - 10.1090/S0002-9939-08-09104-1

M3 - Article

VL - 136

SP - 2019

EP - 2029

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 6

ER -