Preservers for norms of Lie product

Chi Kwong Li, Edward Poon, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)

Abstract

Let {double pipe} · {double pipe} be a unitary similarity invariant norm on the set Mn of n × n complex matrices. A description is obtained for surjective maps φ on Mnsatisfying {double pipe}AB - BA{double pipe} = {double pipe}φ (A)φ (B)-φ (B)φ (A){double pipe} for all A,B ∈ Mn. The general theorem covers the special cases when the norm is one of the Schatten p-norms, the Ky-Fan k-norms, or the k-numerical radii.
Original languageEnglish
Pages (from-to)187-203
Number of pages17
JournalOperators and Matrices
Volume3
Issue number2
DOIs
Publication statusPublished - 1 Jan 2009
Externally publishedYes

Keywords

  • Lie product
  • Unitarily invariant and unitary similarity invariant norms

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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