Corpus ID: 5534637

Non-commutative A-G mean inequality

@article{Hayashi2008NoncommutativeAM,
  title={Non-commutative A-G mean inequality},
  author={T. Hayashi},
  journal={arXiv: Functional Analysis},
  year={2008}
}
  • T. Hayashi
  • Published 2008
  • Mathematics
  • arXiv: Functional Analysis
In this paper we consider non-commutative analogue for the arithmeticgeometric mean inequality $$a^{r}b^{1-r}+(r-1)b\geq ra$$ for two positive numbers $a,b$ and $r> 1$. We show that under some assumptions the non-commutative analogue for $a^{r}b^{1-r}$ which satisfies this inequality is unique and equal to $r$-mean. The case $0<r<1$ is also considered. In particular, we give a new characterization of the geometric mean. 
3 Citations
Functional calculus with operator-monotone functions
A note on the Jensen inequality for self-adjoint operators

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