与Furuta不等式有关的算子单调函数

Operator monotone functions associated with Furuta inequality

运用Furuta不等式和L-H定理给出了与Furuta不等式有关的算子单调函数.对于0≤t≤q,0≤q≤p,算子函数f(t)=At◇q-tp-tBP是递增的;对于0≤t≤2p-q,0≤p≤q<2p,算子函数f(t)=At◇q-tp-tBP是递减的.

Using Furuta inequality and L-H inequality,the paper gives some results associated with the operator monotone functions and the following results are obtained：For 0≤t≤q,0≤q≤p,operator functions f（ t） = A^t◇q-t/p-t B^P is increasing;For 0≤t≤2p- q,0≤p≤q 2p,operator functions f（ t） = A^t◇q-t/p-t B^P is decreasing.