Algebraic reflexivity of isometry groups and automorphism groups of some operator structures

Fernanda Botelho, James Jamison, Lajos Molnár

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Abstract

We establish the algebraic reflexivity of three isometry groups of operator structures: the group of all surjective isometries on the unitary group, the group of all surjective isometries on the set of all positive invertible operators equipped with the Thompson metric, and the group of all surjective isometries on the general linear group of B(H), the operator algebra over a complex infinite dimensional separable Hilbert space H. We show that those isometry groups coincide with certain groups of automorphisms of corresponding structures and hence we also obtain the reflexivity of some automorphism groups.

Original languageEnglish
Pages (from-to)177-195
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume408
Issue number1
DOIs
Publication statusPublished - Dec 1 2013

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Keywords

  • Algebraic reflexivity of transformation groups
  • Automorphisms
  • Hilbert space operators
  • Operator structures
  • Surjective isometries

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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