Jordan triple endomorphisms and isometries of unitary groups

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10 Citations (Scopus)

Abstract

In this paper we present the general form of all continuous endomorphisms of the group Un of n×n complex unitary matrices with respect to the Jordan triple product. These are the continuous maps φ:U n→Un which satisfyφ(VWV)=φ(V)φ(W)φ(V) ,V,W∈Un. The result is applied to determine the structure of certain isometries of Un. These include the isometries relative to any metric given by a unitarily invariant norm on the space Mn of all n×n complex matrices and also the isometries relative to any member of a new class of metrics on Un recently introduced by Chau, Li, Poon and Sze [6].

Original languageEnglish
Pages (from-to)3518-3531
Number of pages14
JournalLinear Algebra and Its Applications
Volume439
Issue number11
DOIs
Publication statusPublished - Dec 1 2013

Keywords

  • Isometries
  • Jordan triple product
  • Unitarily invariant norm
  • Unitary group

ASJC Scopus subject areas

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

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