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eBook details

• Title: On a Reverse of Ando-Hiai Inequality (Report)
• Author : Yuki Seo
• Release Date : January 01, 2010
• Genre: Mathematics,Books,Science & Nature,
• Pages : * pages
• Size : 54 KB

Description

1. INTRODUCTION A (bounded linear) operator A on a Hilbert space H is said to be positive (in symbol: A [greater than or equal to] 0) if (Ax, x) [greater than or equal to] 0 for all x [member of] H. In particular, A 0 means that A is positive and invertible. For some scalars m and M, we write mI [less than or equal to] A [less than or equal to] MI if m(x,x) [less than or equal to] (Ax,x) [less than or equal to] M(x,x) for all x [member of] H. The symbol [parallel] x [parallel] stands for the operator norm. Let A and B be two positive operators on a Hilbert space H. For each [alpha] [member of] [0,1], the weighted geometric mean A [[??].sub.[alpha]] B of A and B in the sense of Kubo-Ando [6] is defined by

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