Multiplicative maps preserving the higher rank numerical ranges and radii

Sean Clark, Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

Let Mnbe the semigroup of n × n complex matrices under the usual multiplication, and let S be different subgroups or semigroups in Mnincluding the (special) unitary group, (special) general linear group, the semigroups of matrices with bounded ranks. Suppose Λk(A) is the rank-k numerical range and rk(A) is the rank-k numerical radius of A ∈ Mn. Multiplicative maps φ{symbol} : S → Mnsatisfying rk(φ{symbol} (A)) = rk(A) are characterized. From these results, one can deduce the structure of multiplicative preservers of Λk(A).
Original languageEnglish
Pages (from-to)2729-2738
Number of pages10
JournalLinear Algebra and Its Applications
Volume432
Issue number11
DOIs
Publication statusPublished - 1 Jun 2010

Keywords

  • Higher rank numerical ranges
  • Multiplicative preservers

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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