### Abstract

Let A and B be C^{*}-algebras with unit and assume that φ{symbol}:A→B is a positive unit preserving linear mapping. Choi proved that {Mathematical expression} if a=a^{*∈A} and Sp(a)⊂(α, β) for every operator convex function f: (α, β) → ℝ. We prove that the equality holds if and only if φ{symbol} restricted to the subalgebra generated by {a} is multiplicative. An example is shown as an application.

Original language | English |
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Pages (from-to) | 744-747 |

Number of pages | 4 |

Journal | Integral Equations and Operator Theory |

Volume | 9 |

Issue number | 5 |

DOIs | |

Publication status | Published - Sep 1986 |

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### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

**On the equality in Jensen's inequality for operator convex functions.** / Petz, D.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 9, no. 5, pp. 744-747. https://doi.org/10.1007/BF01195811

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TY - JOUR

T1 - On the equality in Jensen's inequality for operator convex functions

AU - Petz, D.

PY - 1986/9

Y1 - 1986/9

N2 - Let A and B be C*-algebras with unit and assume that φ{symbol}:A→B is a positive unit preserving linear mapping. Choi proved that {Mathematical expression} if a=a*∈A and Sp(a)⊂(α, β) for every operator convex function f: (α, β) → ℝ. We prove that the equality holds if and only if φ{symbol} restricted to the subalgebra generated by {a} is multiplicative. An example is shown as an application.

AB - Let A and B be C*-algebras with unit and assume that φ{symbol}:A→B is a positive unit preserving linear mapping. Choi proved that {Mathematical expression} if a=a*∈A and Sp(a)⊂(α, β) for every operator convex function f: (α, β) → ℝ. We prove that the equality holds if and only if φ{symbol} restricted to the subalgebra generated by {a} is multiplicative. An example is shown as an application.

UR - http://www.scopus.com/inward/record.url?scp=34250131594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250131594&partnerID=8YFLogxK

U2 - 10.1007/BF01195811

DO - 10.1007/BF01195811

M3 - Article

AN - SCOPUS:34250131594

VL - 9

SP - 744

EP - 747

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 5

ER -