三类自伴映射的性质

Properties and three hermitian maps on the matrix spaces

构造了三类从矩阵空间Mn到自身的保持矩阵自伴性的映射,主要研究了这三类映射之间交换性的等价关系与等价条件,完全有界范数的上界刻画及它们谱的结构特征。同时,应用这些映射在张量积空间中,讨论了一类与量子信息论紧密相关的算子的性质,给出了其迹范数上下界的估计。

The properties of three kinds Hermitian maps from Mn into Mn are investigated, such as equivalence relation and equivalent condition of commutativity, the bound of the completely hounded norm and spectrum, structure and characteristic of spectrum. Moreover, properties of operators which is related to quantum information theory are discussed, the bound of two operators on the space of H H is estimated.