Transformations of the unitary group on a Hilbert space

Lajos Molnár, Peter Šemrl

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

Let H be an infinite dimensional separable complex Hilbert space and . U be the group of all unitary operators on . H. Motivated by the algebraic properties of surjective isometries of . U that have recently been revealed, and also by some classical results related to automorphisms of the unitary groups of operator algebras, we determine the structures of bijective transformations of . U that respect certain algebraic operations. These are, among others, the usual product of operators, the Jordan triple product, the inverted Jordan triple product, and the multiplicative commutator. Our basic approach to obtain these results is the use of commutativity preserving transformations on the unitary group.

Original languageEnglish
Pages (from-to)1205-1217
Number of pages13
JournalJournal of Mathematical Analysis and Applications
Volume388
Issue number2
DOIs
Publication statusPublished - Apr 15 2012

Keywords

  • Automorphisms
  • Commutativity preserving maps
  • Hilbert space
  • Unitary group

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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