### Abstract

In this paper we consider three operations on positive definite cones of C^{⁎}-algebras which are related to weighted geometric means and appear in the formulas defining various versions of quantum Rényi relative entropy. We show how Jordan *-isomorphisms between C^{⁎}-algebras can be characterized by the preservation of the norms of products under those operations or by the preservation of the operations themselves. We also obtain conditions for the commutativity of the underlying algebras by showing that we have that property if one of the quantities under considerations can be transformed by a surjective map to another different such quantity.

Original language | English |
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Pages (from-to) | 364-390 |

Number of pages | 27 |

Journal | Linear Algebra and Its Applications |

Volume | 588 |

DOIs | |

Publication status | Published - márc. 1 2020 |

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### ASJC Scopus subject areas

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

### Cite this

**Characterizations of Jordan *-isomorphisms of C ^{⁎}-algebras by weighted geometric mean related operations and quantities.** / Chabbabi, Fadil; Mbekhta, Mostafa; Molnár, Lajos.

Research output: Article

^{⁎}-algebras by weighted geometric mean related operations and quantities',

*Linear Algebra and Its Applications*, vol. 588, pp. 364-390. https://doi.org/10.1016/j.laa.2019.11.024

^{⁎}-algebras by weighted geometric mean related operations and quantities. Linear Algebra and Its Applications. 2020 márc. 1;588:364-390. https://doi.org/10.1016/j.laa.2019.11.024

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TY - JOUR

T1 - Characterizations of Jordan *-isomorphisms of C⁎-algebras by weighted geometric mean related operations and quantities

AU - Chabbabi, Fadil

AU - Mbekhta, Mostafa

AU - Molnár, Lajos

PY - 2020/3/1

Y1 - 2020/3/1

N2 - In this paper we consider three operations on positive definite cones of C⁎-algebras which are related to weighted geometric means and appear in the formulas defining various versions of quantum Rényi relative entropy. We show how Jordan *-isomorphisms between C⁎-algebras can be characterized by the preservation of the norms of products under those operations or by the preservation of the operations themselves. We also obtain conditions for the commutativity of the underlying algebras by showing that we have that property if one of the quantities under considerations can be transformed by a surjective map to another different such quantity.

AB - In this paper we consider three operations on positive definite cones of C⁎-algebras which are related to weighted geometric means and appear in the formulas defining various versions of quantum Rényi relative entropy. We show how Jordan *-isomorphisms between C⁎-algebras can be characterized by the preservation of the norms of products under those operations or by the preservation of the operations themselves. We also obtain conditions for the commutativity of the underlying algebras by showing that we have that property if one of the quantities under considerations can be transformed by a surjective map to another different such quantity.

KW - C-algebra

KW - Jordan -isomorphism

KW - Operator means

KW - Positive definite cone

KW - Preservers

KW - Weighted geometric means

UR - http://www.scopus.com/inward/record.url?scp=85076174542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85076174542&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2019.11.024

DO - 10.1016/j.laa.2019.11.024

M3 - Article

AN - SCOPUS:85076174542

VL - 588

SP - 364

EP - 390

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -