冯·诺依曼子代数的分离投影

The Separating Projection of von Neumann Subalgebras

引入了冯·诺依曼代数的子代数的分离投影的概念,然后刻画了矩阵代数中其子代数分离投影的存在性,构造了可分无限Hilbert特空间上子代数的分离投影。具体地,设M=M_n(C)M_n(C),N=M_n(C)C1_n,证明了N在M中存在维数为r(1≤r≤n^2-1)的分离投影。

This article first introduces the concept of the separating projection of a von Neumann subalgebra in a von Neumann algebra,and explores the existence of the separating projection of a subalgebra in a matrix algebra. Then an example of the existence of the separating projection for a separable infinite dimensional Hilbert space is constructed.