Multiplicative Jordan triple isomorphisms on the self-adjoint elements of von Neumann algebras

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

In this paper we consider multiplicative Jordan triple isomorphisms between the sets of self-adjoint elements (respectively the sets of positive elements) of von Neumann algebras. These transformations are the bijective maps which satisfy the equalityφ{symbol} (ABA) = φ{symbol} (A) φ{symbol} (B) φ{symbol} (A)on their domains. We show that all those transformations originate from linear *-algebra isomorphisms and linear *-algebra antiisomorphisms in the case when the underlying von Neumann algebras do not have commutative direct summands. An application of our results concerning non-linear maps which preserve the absolute value of products is also presented.

Original languageEnglish
Pages (from-to)586-600
Number of pages15
JournalLinear Algebra and Its Applications
Volume419
Issue number2-3
DOIs
Publication statusPublished - Dec 1 2006

Fingerprint

Linear algebra
Von Neumann Algebra
Algebra
Isomorphism
Multiplicative
Nonlinear Map
Bijective
Absolute value
Equality

Keywords

  • Multiplicative Jordan triple isomorphism
  • Positive operator
  • Self-adjoint operator
  • von Neumann algebra

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Multiplicative Jordan triple isomorphisms on the self-adjoint elements of von Neumann algebras. / Molnár, L.

In: Linear Algebra and Its Applications, Vol. 419, No. 2-3, 01.12.2006, p. 586-600.

Research output: Contribution to journalArticle

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