算子广义谱几何平均的若干结果

Some Conclusions about Generalized Spectral Geometric Mean of two Positive Operators

1997年Fiedler和Ptak定义和研究了正定矩阵间的谱几何平均F(A,B),并给出了相关性质.这里构造的正算子间的广义谱几何平均Eα(A,B)进一步延续和拓展了Fiedler和Ptak的理论,并且通过古田不等式得到一系列比谱几何平均F(A,B)更为一般的结果.

In 1997,Fiedler and Pta＇k introduced spectral geometric mean F（A,B）of positive definite matrixes,and discuss its properties.In this note we will introduce the generalized spectral geometric mean of two positive operators Eα（A,B）and to extend their theorems.In addition,we show some comparison theorems on Eα（A,B）by virtue of the Furuta Inequality.