Article ID Journal Published Year Pages File Type
4602963 Linear Algebra and its Applications 2006 5 Pages PDF
Abstract

Let A, B > 0, the positive operators on a Hilbert space. Ando–Hiai inequality (AH) and Furuta inequality (F) are given as follows:equation(AH)A,B>0;A♯αB⩽I⇒Ar♯αBr⩽Iforr⩾1,andequation(F)A⩾B>0⇒A-r♯1+rp+rBp⩽B⩽A.We show these inequalities imply each other.

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Physical Sciences and Engineering Mathematics Algebra and Number Theory
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Ando–Hiai inequality and Furuta inequality
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