Inclusion regions for numerical ranges and linear preservers

C. K. Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Let R be a proper subset of the complex plane, and let SRbe the set of n × n complex matrices A such that the numerical range W(A) satisfies W(A) ⊆ R. Linear maps φ on matrices satisfying φ(SR) = SRare characterized. Denote by S̃Rthe set of n × n complex matrices A such that the numerical radius r(A) satisfies r(A) ⊆ R for a proper subset R of nonnegative real numbers. Linear maps φ on matrices satisfying φ(S̃R) = S̃Rare also characterized. Analogous results on Hermitian matrices are obtained.
Original languageEnglish
Pages (from-to)235-249
Number of pages15
JournalLinear and Multilinear Algebra
Volume52
Issue number3-4
DOIs
Publication statusPublished - 1 Jan 2004
Externally publishedYes

Keywords

  • Hermitian matrices
  • Linear maps
  • Numerical range (radius)

ASJC Scopus subject areas

  • Algebra and Number Theory

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