Maps preserving the geometric mean of positive operators

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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 1 2009

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Keywords

  • Automorphism
  • Geometric mean
  • Positive operators

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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