Maps preserving the geometric mean of positive operators

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let H be a complex Hilbert space. The symbol A#B stands for the geometric mean of the positive bounded linear operators A, B on H in the sense of Ando. In this paper we describe the general form of all automorphisms of the set of positive operators with respect to the operation #. We prove that if dim H ≥ 2, any such transformation is implemented by an invertible bounded linear or conjugate-linear operator on H.

Original languageEnglish
Pages (from-to)1763-1770
Number of pages8
JournalProceedings of the American Mathematical Society
Volume137
Issue number5
DOIs
Publication statusPublished - May 2009

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Positive Linear Operators
Geometric mean
Hilbert spaces
Positive Operator
Bounded Linear Operator
Invertible
Linear Operator
Mathematical operators
Automorphisms
Hilbert space
Form

Keywords

  • Automorphism
  • Geometric mean
  • Positive operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Maps preserving the geometric mean of positive operators. / Molnár, L.

In: Proceedings of the American Mathematical Society, Vol. 137, No. 5, 05.2009, p. 1763-1770.

Research output: Contribution to journalArticle

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