What is a Murray-von Neumann algebra?

Abstract: It was observed by Murray and von Neumann in their seminal paper on rings of operators (1936) that the set of closed, densely-defined operators affiliated with a finite von Neumann algebra has the structure of a *-algebra. The algebra of affiliated operators naturally appears in many contexts; for instance, in the setting of group von Neumann algebras in the study of non-compact spaces and infinite group actions. In this talk, we will give an intrinsic description of Murray-von Neumann algebras avoiding reference to a Hilbert space, thus, revealing the intrinsic nature of various notions associated with such affiliated operators. In fact, we will view Murray-von Neumann algebras as ordered complex topological *-algebras arising from a functorial construction over finite von Neumann algebras.

functional analysisoperator algebras

Audience: researchers in the topic

Webinars on Operator Theory and Operator Algebras