von Neumann代数交叉积的注记

A Note on Crossed Products over von Neumann Algebras

设A是B(H)中的极大交换*-子代数, G是离散群,在不要求G自由地作用在A的情况下,得到了交叉积A×αG是因子的充分且必要条件.

In this note, we obtain the sufficient and necessary condition of crossed product A×α G, where A is a maximal abelian *-subalgebra of B(H) and G is a discrete group, to be a factor without assuming that G acts freely on A.