### 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 2009 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 137, no. 5, pp. 1763-1770. https://doi.org/10.1090/S0002-9939-08-09749-9

}

TY - JOUR

T1 - Maps preserving the geometric mean of positive operators

AU - Molnár, L.

PY - 2009/5

Y1 - 2009/5

N2 - 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.

AB - 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.

KW - Automorphism

KW - Geometric mean

KW - Positive operators

UR - http://www.scopus.com/inward/record.url?scp=64649096789&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=64649096789&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-08-09749-9

DO - 10.1090/S0002-9939-08-09749-9

M3 - Article

VL - 137

SP - 1763

EP - 1770

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 5

ER -