论文标题
加权几何平均值的操作员不平等和陀螺
Operator inequalities and gyrolines of the weighted geometric means
论文作者
论文摘要
我们在本文中考虑了正确定运算符的两种不同类型的加权几何方法。我们显示了这些几何均值的组成部分，并具有光谱几何均值作为度量中点的几何特性。此外，将显示一些与积极确定运算符的几何方式相关的有趣的不平等。我们还看到具有有限尺寸的陀螺仪结构中加权几何平均值的含义，并找到2 by-2阳性确定矩阵和密度矩阵的加权几何均值的公式。
We consider in this paper two different types of the weighted geometric means of positive definite operators. We show the component-wise bijection of these geometric means and give a geometric property of the spectral geometric mean as a metric midpoint. Moreover, several interesting inequalities related with the geometric means of positive definite operators will be shown. We also see the meaning of weighted geometric means in the gyrogroup structure with finite dimension and find the formulas of weighted geometric means of 2-by-2 positive definite matrices and density matrices.
