### Abstract

Let T be a normal semifinite trace on a von Neumann algebra, and let f be a continuous convex function on the interval [0, ∞) with f(0) = 0. For a positive element a of the algebra and a positive contraction α on the algebra, the following inequality is obtained: T(f(α(a))) ≤ T(α(f(a))).

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

Pages (from-to) | 273-277 |

Number of pages | 5 |

Journal | Proceedings of the American Mathematical Society |

Volume | 99 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1987 |

### Fingerprint

### Keywords

- Convex function
- Jensen’s inequality
- Trace
- Von Neumann algebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Jensen’s inequality for positive contractions on operator algebras.** / Petz, D.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Jensen’s inequality for positive contractions on operator algebras

AU - Petz, D.

PY - 1987

Y1 - 1987

N2 - Let T be a normal semifinite trace on a von Neumann algebra, and let f be a continuous convex function on the interval [0, ∞) with f(0) = 0. For a positive element a of the algebra and a positive contraction α on the algebra, the following inequality is obtained: T(f(α(a))) ≤ T(α(f(a))).

AB - Let T be a normal semifinite trace on a von Neumann algebra, and let f be a continuous convex function on the interval [0, ∞) with f(0) = 0. For a positive element a of the algebra and a positive contraction α on the algebra, the following inequality is obtained: T(f(α(a))) ≤ T(α(f(a))).

KW - Convex function

KW - Jensen’s inequality

KW - Trace

KW - Von Neumann algebra

UR - http://www.scopus.com/inward/record.url?scp=84968476234&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84968476234&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1987-0870784-0

DO - 10.1090/S0002-9939-1987-0870784-0

M3 - Article

VL - 99

SP - 273

EP - 277

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 2

ER -