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Abstract: In this paper we consider non-commutative analogue for thearithmeticgeometric mean inequality $$a^{r}b^{1-r}+r-1b\geq ra$$ for twopositive numbers $a,b$ and $r> 1$. We show that under some assumptions thenon-commutative analogue for $a^{r}b^{1-r}$ which satisfies this inequality isunique and equal to $r$-mean. The case $0


Autor: Tomohiro Hayashi

Fuente: https://arxiv.org/







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