Elementary operators on self-adjoint operators

L. Molnár, Peter Šemrl

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let H be a Hilbert space and let A and B be standard *-operator algebras on H. Denote by As and Bs the set of all self-adjoint operators in A and B, respectively. Assume that M : As → Bs and M* : Bs → As are surjective maps such that M (A M* (B) A) = M (A) B M (A) and M* (B M (A) B) = M* (B) A M* (B) for every pair A ∈ As, B ∈ Bs. Then there exist an invertible bounded linear or conjugate-linear operator T : H → H and a constant c ∈ {- 1, 1} such that M (A) = c T A T*, A ∈ As, and M* (B) = c T* B T, B ∈ Bs.

Original languageEnglish
Pages (from-to)302-309
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Volume327
Issue number1
DOIs
Publication statusPublished - Mar 1 2007

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Standard Operator Algebra
Elementary Operators
Hilbert spaces
Self-adjoint Operator
Invertible
Algebra
Linear Operator
Mathematical operators
Hilbert space
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Keywords

  • Elementary operator of length one
  • Self-adjoint operator
  • Standard *-operator algebra

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Elementary operators on self-adjoint operators. / Molnár, L.; Šemrl, Peter.

In: Journal of Mathematical Analysis and Applications, Vol. 327, No. 1, 01.03.2007, p. 302-309.

Research output: Contribution to journalArticle

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