关于多个算子的Furuta型算子单调函数

On the Furuta-type Operator Monotonic Function for Several Operators

设p≥1,且A、B是Hilbert空间上两个正算子,T.Furuta给出若A≥B>0,那么对任意t∈[0,1]有,G(r,s)=A-r/2{Ar/2(A-t/2BpA-t/2)sAr/2}1-t+r/(p-t)+srA-r/2是关于r,s在r≥t及s≥1上单调递减的,我们给出该结果可以推广到多个算子的情形.

Furutashowed that if A≥B〉0, then for a fixed p≥1 and t∈[0,1,G（r,s）=A^-r/2{A^r/2（A^-r/2BpA^r/2）^1-t＋r/（p-t）s＋rA^-r/2 is a decreasing function of both r and s for all r≥t and s≥1. In this paper, we give a similar result about several operators.