### Abstract

Let f: ℝ^{+} → ℝ. The subject is the trace inequality Tr f(A) + Tr f(P_{2}AP_{2}) ≦ Tr f(P_{12}AP_{12}) + Tr f(P_{23}AP_{23}), where A is a positive operator, P_{1}; P_{2}; P_{3} are orthogonal projections such that P_{1} + P_{2} + P_{3} = I, P_{12} = P_{1} + P_{2} and P_{23} = P_{2} + P_{3}. There are several examples of functions f satisfying the inequality (called (SSA)) and the case of equality is described.

Original language | English |
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Pages (from-to) | 386-394 |

Number of pages | 9 |

Journal | Acta Mathematica Hungarica |

Volume | 128 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 15 2010 |

### Keywords

- Operator concave functions
- Operator monotone functions
- Strong subadditivity
- Trace inequality

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Audenaert, K., Hiai, F., & Petz, D. (2010). Strongly subadditive functions.

*Acta Mathematica Hungarica*,*128*(4), 386-394. https://doi.org/10.1007/s10474-010-9222-7