关于多个算子的Furuta型算子单调函数

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.

On the Furuta-type Operator Monotonic Function for Several Operators

Furutashowed that if AB>0, then for a fixed p1 and t∈,G(r,s)=A-r2{Ar2(A-t2BpA-t2)sAr2}1-t+r(p-t)s+rA-r2 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.