### Abstract

We describe the precise structure of all surjective (’a priori’ nonlinear or, better say, nonaffine) Bures isometries between density spaces of C^{⁎}-algebras equipped with faithful traces. It turns out that those maps are closely related to (linear) Jordan *-isomorphisms between the underlying algebras. Beside density spaces, we consider the problem also on the positive definite (and positive semidefinite) cones of C^{⁎}-algebras.

Original language | English |
---|---|

Pages (from-to) | 22-33 |

Number of pages | 12 |

Journal | Linear Algebra and Its Applications |

Volume | 557 |

DOIs | |

Publication status | Published - Nov 15 2018 |

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### Keywords

- Bures metric
- C-algebra
- Density space
- Fidelity
- Positive cone
- Preservers

### ASJC Scopus subject areas

- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics

### Cite this

**Bures isometries between density spaces of C ^{⁎}-algebras.** / Molnár, L.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Bures isometries between density spaces of C⁎-algebras

AU - Molnár, L.

PY - 2018/11/15

Y1 - 2018/11/15

N2 - We describe the precise structure of all surjective (’a priori’ nonlinear or, better say, nonaffine) Bures isometries between density spaces of C⁎-algebras equipped with faithful traces. It turns out that those maps are closely related to (linear) Jordan *-isomorphisms between the underlying algebras. Beside density spaces, we consider the problem also on the positive definite (and positive semidefinite) cones of C⁎-algebras.

AB - We describe the precise structure of all surjective (’a priori’ nonlinear or, better say, nonaffine) Bures isometries between density spaces of C⁎-algebras equipped with faithful traces. It turns out that those maps are closely related to (linear) Jordan *-isomorphisms between the underlying algebras. Beside density spaces, we consider the problem also on the positive definite (and positive semidefinite) cones of C⁎-algebras.

KW - Bures metric

KW - C-algebra

KW - Density space

KW - Fidelity

KW - Positive cone

KW - Preservers

UR - http://www.scopus.com/inward/record.url?scp=85050478126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85050478126&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2018.07.008

DO - 10.1016/j.laa.2018.07.008

M3 - Article

VL - 557

SP - 22

EP - 33

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -