Asymptotic properties of von Neumann algebras (Q1094642)

This is thorough review (consisting of five sections) of the construction, properties of use of the asymptotic algebra \(C^ U_ M\) associated to a factor M and a free ultrafilter U on \({\mathbb{N}}\). It presents first (in Sections 1 and 2) a detailed background on the modular theory, including some completions to author's previous results. The relevance of the structure of \(C^ U_ M\) to the analysis of M is described in the last two sections (including solutions to some problems of Connes and Woods on asymptotic abelianess of type III factors).