### Abstract

Some functions f: ℝ^{+}→ ℝ^{+} induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping J_{D}^{f-1}:M_{n}→M_{n} on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of J_{D} ^{f-1} in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.

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

Pages (from-to) | 984-997 |

Number of pages | 14 |

Journal | Linear Algebra and Its Applications |

Volume | 435 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 1 2011 |

### Fingerprint

### Keywords

- Completely positive mapping
- Hadamard product
- Logarithmic mean
- Matrix means
- Matrix monotone function

### ASJC Scopus subject areas

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

### Cite this

*Linear Algebra and Its Applications*,

*435*(5), 984-997. https://doi.org/10.1016/j.laa.2011.01.043

**Completely positive mappings and mean matrices.** / Besenyei, Ádám; Petz, D.

Research output: Contribution to journal › Article

*Linear Algebra and Its Applications*, vol. 435, no. 5, pp. 984-997. https://doi.org/10.1016/j.laa.2011.01.043

}

TY - JOUR

T1 - Completely positive mappings and mean matrices

AU - Besenyei, Ádám

AU - Petz, D.

PY - 2011/9/1

Y1 - 2011/9/1

N2 - Some functions f: ℝ+→ ℝ+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping JDf-1:Mn→Mn on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of JD f-1 in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.

AB - Some functions f: ℝ+→ ℝ+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping JDf-1:Mn→Mn on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of JD f-1 in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.

KW - Completely positive mapping

KW - Hadamard product

KW - Logarithmic mean

KW - Matrix means

KW - Matrix monotone function

UR - http://www.scopus.com/inward/record.url?scp=79958793902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79958793902&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2011.01.043

DO - 10.1016/j.laa.2011.01.043

M3 - Article

AN - SCOPUS:79958793902

VL - 435

SP - 984

EP - 997

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 5

ER -