Unitary similarity invariant function preservers of skew products of operators

Jianlian Cui, Chi Kwong Li, Nung Sing Sze

Research output: Journal article publicationJournal articleAcademic researchpeer-review

6 Citations (Scopus)

Abstract

Suppose F(⋅) is a unitary invariant norm, the pseudo spectra, the pseudo spectral radius, the C-numerical range, or the C-numerical radius for some finite rank operator C. The structure is determined for surjective maps Φ:A→B satisfying F(A⁎B)=F(Φ(A)⁎Φ(B)) for all A,B∈A. To establish the proofs, some general results are obtained for functions F:F1(H)∪{0}→[0,+∞), where F1(H) is the set of rank one operators in B(H), satisfying (a) F(μUAU⁎)=F(A) for a complex unit μ, A∈F1(H) and unitary U∈B(H), (b) for any rank one operator X∈F1(H) the map t↦F(tX) on [0,∞) is strictly increasing, and (c) the set {F(X):X∈F1(H) and ‖X‖=1} attains its maximum and minimum.
Original languageEnglish
Pages (from-to)716-729
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume454
Issue number2
DOIs
Publication statusPublished - 15 Oct 2017

Keywords

  • Generalized numerical radius
  • Pseudo spectrum
  • Unitary similarity invariant function

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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