凹函数在算子迹中的一个应用

The application of concave function in trace operator

算子迹是矩阵分析学中的一个很重要的概念,并且在物理学中有很重要的应用,例如著名的Lieb凸定理就是在算子迹下来研究矩阵函数的结合凸性质的.在算子迹的作用下,凹函数的定义域可以从实数推广到一般的厄米算子上,得到一些很有用的结论.利用凹函数的性质,研究了有关算子迹的一些不等式,并且结合算子单调函数的概念,做了一些相应的推广.

Trace operator is a very important concept in matrix analysis and has very important applications in physics.For example,the Lieb concave theorem gives the combined concave properties of matrix functions under trace operator.By using trace operator,the domain of concave function can be generalized to Hermite operator,and some useful conclusions can be obtained.This paper uses the concept of the concave function to study some inequalities related to the trace operator,and obtains some generalizations of inequalities associated with the operator monotone function.