Isometries of the unitary groups and Thompson isometries of the spaces of invertible positive elements in C*-algebras

Osamu Hatori, Lajos Molnár

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

We show that the existence of a surjective isometry (which is merely a distance preserving map) between the unitary groups of unital C*-algebras implies the existence of a Jordan *-isomorphism between the algebras. In the case of von Neumann algebras we describe the structure of those isometries showing that any of them is extendible to a real linear Jordan *-isomorphism between the underlying algebras multiplied by a fixed unitary element. We present a result of similar spirit for the surjective Thompson isometries between the spaces of all invertible positive elements in unital C*-algebras.

Original languageEnglish
Pages (from-to)158-167
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume409
Issue number1
DOIs
Publication statusPublished - Jan 1 2014

Keywords

  • -isomorphism
  • C-algebra
  • Function algebra
  • Isometry
  • Jordan
  • Positive element
  • Thompson metric
  • Unitary group
  • Von Neumann algebra

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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