### 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 language | English |
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Pages (from-to) | 1763-1770 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2009 |

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### Keywords

- Automorphism
- Geometric mean
- Positive operators

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics