关于迹类算子的几个不等式

Some inequalities in trace-class operators

利用算子的极分解证明无穷维 H ilbert空间 H上正迹类算子迹的不等式 ,又对于 H H上的正算子矩阵 ,当主对角线元素 L、M的正次幂 Lp、Mp(p >0 )为迹类算子或 Hilbert-Schmidt算子时 ,利用正算子矩阵的某些性质及 H.Wayl的不等式 ,分别得到迹范数不等式和 Hilber-Schmidt范数不等式 ,从而使作为有限维空间上算子的矩阵或分块矩阵的有关结论得到推广。

By using the polar decomposition of operator,an inequality is shown in trace of positive trace class operator.For positive matrix of operator on HH,an inequality in trace norm and an inequality in Hilbert Schmidt norm are obtained,respectively,according to some results of positive matrix of operator and H Weyl's inequality.As a result, some conclusions in literature concerned have been generalized when matrix or block matrix is regarded as operator of finite dimension Hilbert space.