冯诺依曼代数的建立与发展

A brief history of von Neumann algebras

通过文献调研,对von Neumann代数建立与发展进程中的重要事件进行系统梳理。Murry和von Neumann在二十世纪三四十年代做出了奠基性工作:双交换子定理、不完全的因子分类理论、以及群von Neumann代数和群-测度空间构造这两类典型的II-1因子。20世纪70年代Tomita-Takesaki理论、Connes关于顺从von Neumann因子的分类工作使得von Neumann代数不断发展完善。

Systematically study the important events during the creation and development of von Neumann algebra through literature research. The results show that Murry and von Neumann did fundamental work on the theory: the double commutant theorem,unfinished classification of factors,and two basic constructions of type II-1 factors( group von Neumann algebras and group-measure space construction von Neumann algebras).Tomita-Takesaki theory,A. Connes' amenable von Neumann algebra theory in 1970' s and V. Jones' index theory for sub-factors in 1980 s' made von Neumann algebra more improved and matured.