### Abstract

We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

Original language | English |
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Pages (from-to) | 451-463 |

Number of pages | 13 |

Journal | Acta Scientiarum Mathematicarum |

Volume | 84 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Geodesic correspondence
- Operator means
- Positive definite cone
- Preservers

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence.** / Molnár, L.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Maps between the positive definite cones of operator algebras preserving a norm of a geodesic correspondence

AU - Molnár, L.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

AB - We prove that any bijective map between the positive definite cones of von Neumann algebras which preserves a certain unitarily invariant norm of a particular weighted geometric mean of elements is essentially (up to two-sided multiplication by an invertible positive element) equal to the restriction of a Jordan *-isomorphism between the algebras.

KW - Geodesic correspondence

KW - Operator means

KW - Positive definite cone

KW - Preservers

UR - http://www.scopus.com/inward/record.url?scp=85057730558&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85057730558&partnerID=8YFLogxK

U2 - 10.14232/actasm-018-514-x

DO - 10.14232/actasm-018-514-x

M3 - Article

AN - SCOPUS:85057730558

VL - 84

SP - 451

EP - 463

JO - Acta Scientiarum Mathematicarum

JF - Acta Scientiarum Mathematicarum

SN - 0001-6969

IS - 3-4

ER -