An operator inequality related to Jensen's 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

An operator inequality related to Jensen's inequality

Authors:	Mitsuru Uchiyama

Affiliation:	Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, 811-4192, Japan

Abstract:	For bounded non-negative operators and , Furuta showed $begin{displaymath}0leq A leq B {rm implies } A^{frac{r}{2}}B^sA^{frac{r}{2... ... A^{frac{r}{2}})^{frac{s+r}{t+r}} (0leq r, 0leq s leq t).end{displaymath}$ We will extend this as follows: implies $begin{displaymath}A^{frac{r}{2}}(lambda B^s+ (1-lambda)C^s)A^{frac{r}{2}} ... ...bda B^t+ (1- lambda)C^t) A^{frac{r}{2}}}^{frac{s+r}{t+r}} ,end{displaymath}$ where is a harmonic mean of and . The idea of the proof comes from Jensen's inequality for an operator convex function by Hansen-Pedersen.

Keywords:	Order of selfadjoint operators Jensen inequality Furuta inequality

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载全文