Generalized Sunder inequality

Sangeeta Jhanjee, Alan James Pryde

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

Abstract

V. Sunder proved that for n×n complex matrices A and B, with A being Hermitian and B being skew Hermitian with eigenvalues {αi}ni=1{αi}i=1n and {βi}ni=1{βi}i=1n respectively (counting multiplicity) such that
|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|
|α1|≥⋯≥|αn|,|β1|≤⋯≤|βn|
then
|αi−βi|≤∥A−B∥
|αi−βi|≤∥A−B∥
where ∥⋅∥∥⋅∥ is the operator bound norm. We generalize Sunder’s result to the case of an m-tuple of n × n complex matrices, using the Clifford operator.
Original languageEnglish
Title of host publicationOperator Algebras and Mathematical Physics: 24th International Workshop in Operator Theory and its Applications, Bangalore, December 2013 (IWOTA 2013)
EditorsTirthankar Bhattacharyya, Michael A Dritschel
Place of PublicationCham Switzerland
PublisherSpringer
Pages83-86
Number of pages4
Volume247
ISBN (Electronic)9783319181820
ISBN (Print)9783319181813
DOIs
Publication statusPublished - 2015
EventInternational Workshop on Operator Theory and its Applications (IWOTA) 2013 - Indian Institute of Science, Bangalore, India
Duration: 16 Dec 201320 Dec 2013
Conference number: 24th
http://math.iisc.ernet.in/~iwota2013/

Workshop

WorkshopInternational Workshop on Operator Theory and its Applications (IWOTA) 2013
Abbreviated titleIWOTA 2013
CountryIndia
CityBangalore
Period16/12/1320/12/13
Internet address

Keywords

  • Joint eigenvalues
  • joint spectra
  • Clifford algebra
  • commuting tuple of matrices
  • Sunder’s inequality

Cite this

Jhanjee, S., & Pryde, A. J. (2015). Generalized Sunder inequality. In T. Bhattacharyya, & M. A. Dritschel (Eds.), Operator Algebras and Mathematical Physics: 24th International Workshop in Operator Theory and its Applications, Bangalore, December 2013 (IWOTA 2013) (Vol. 247, pp. 83-86). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-18182-0_5