### 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 | |

State | Published - Jun 1 2008 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*136*(6), 2019-2029. https://doi.org/10.1090/S0002-9939-08-09104-1

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

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 136, no. 6, pp. 2019-2029. https://doi.org/10.1090/S0002-9939-08-09104-1

}

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 -