Mean theoretic approach to the grand Furuta inequality期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Mean theoretic approach to the grand Furuta inequality

Authors:	Masatoshi Fujii Eizaburo Kamei

Institution:	Department of Mathematics, Osaka Kyoiku University, Asahigaoka, Kashiwara, Osaka 582, Japan ; Momodani Senior Highschool, Ikuno, Osaka 544, Japan

Abstract:	Very recently, Furuta obtained the grand Furuta inequality which is a parameteric formula interpolating the Furuta inequality and the Ando-Hiai inequality as follows : If $A \ge B \ge 0$ and is invertible, then for each $t \in 0,1]$ , $\begin{equation}F_{p,t}(A,B,r,s) = A^{-r/2}\{A^{r/2}(A^{-t/2}B^{p}A^{-t/2})^{s}A ^{r/2}\}^{\frac {1-t+r}{(p-t)s+r}}A^{-r/2} \end{equation}$ is a decreasing function of both and for all $r \ge t, ~p \ge 1$ and $s \ge 1$ . In this note, we employ a mean theoretic approach to the grand Furuta inequality. Consequently we propose a basic inequality, by which we present a simple proof of the grand Furuta inequality.

Keywords:	Positive operators L\"{o}wner-Heinz inequality Furuta inequality Ando-Hiai inequality grand Furuta inequality

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