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

Fernanda Botelho, James Jamison, L. Molnár

Research output: Contribution to journalArticle

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

Fingerprint

Reflexivity
Isometry Group
Hilbert spaces
Automorphism Group
Algebra
Mathematical operators
Isometry
Operator
General Linear Group
Separable Hilbert Space
Operator Algebras
Unitary group
Invertible
Automorphisms
Metric

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Algebraic reflexivity of isometry groups and automorphism groups of some operator structures. / Botelho, Fernanda; Jamison, James; Molnár, L.

In: Journal of Mathematical Analysis and Applications, Vol. 408, No. 1, 01.12.2013, p. 177-195.

Research output: Contribution to journalArticle

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