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

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