@article{1186.47014,
author="Seo, Yuki",
title="{On a reverse of Ando-Hiai inequality.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="1",
pages="87-91",
year="2010",
abstract="{Summary: We show a complement of the Ando-Hiai inequality: Let $A$
    and $B$ be positive invertible operators on a Hilbert space $H$ and
    $\alpha\in[0,1]$. If $A\sharp_\alpha B\le I$, then
 $$A^r\sharp_\alpha
    B^r\le \|(A\sharp_\alpha B)^{-1}\|^{1-r}I \quad\text{for all }0<r\le 1,$$
    where $I$ is the identity operator and $\|\cdot\|$ stands for the operator
    norm.}",
keywords="{Ando-Hiai inequality; positive operator; geometric mean}",
classmath="{*47A63 (Operator inequalities, etc.)
47A30 (Operator norms and inequalities)
47A64 (Operator means etc.)
}",
}