Characterizations of log<i>A</i>≥log<i>B</i> and normaloid operators via Heinz 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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Characterizations of logA≥logB and normaloid operators via Heinz inequality

Authors:	Takeaki Yamazaki

Institution:	(1) Department of Mathematics, Kanagawa University, 221-8686 Yokohama, Japan

Abstract:	In 1951, Heinz showed the following useful norm inequality:If A, B0and XB(H), then AXB ^rX^1–rA ^r XB ^rholds for r 0, 1]. In this paper, we shall show the following two applications of this inequality:Firstly, by using Furuta inequality, we shall show an extension of Cordes inequality. And we shall show a characterization of chaotic order (i.e., logAlogB) by a norm inequality.Secondly, we shall study the condition under which $\parallel T\parallel = \parallel \tilde T\parallel$ , where $\tilde T = \|T\|^{\tfrac{1}{2}} U\|T\|^{\tfrac{1}{2}}$ is Aluthge transformation ofT. Moreover we shall show a characterization of normaloid operators (i.e.,r(T)=T) via Aluthge transformation.

Keywords:	Primary 47A30 Secondly 47A63 47A64 47B20
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