The injective factors of type \(III_{\lambda}\), \(0<\lambda <1\)
The author gives a new proof of A. Connes' old result that there is only one injective factor of type \(III_{\lambda}\) for each \(\lambda\), \(0<\lambda <1\). The proof is more direct than the one of Connes and avoids the analysis of outer conjugacy classes of automorphisms of factors. Steps in the proof are a technical result giving a necessary condition for two n-tuples of unit vectors in a Hilbert \(W^*\)-bimodule to be almost unitarily equivalent and a strong version of Dixmier's approximation theorem for \(III_{\lambda}\) factors. This article is part of a series of papers where the author approaches Connes' results on injective factors using systematically completely positive maps and where he obtains very important simplifications and additions to Connes' theory.
injective factor of type \(III_{\lambda }\)
avoids the analysis of outer conjugacy classes of automorphisms of
Dixmier's approximation theorem for \(III_{\lambda }\) factors
avoids the analysis of outer conjugacy classes of automorphisms of factors
scientific article; zbMATH DE number 4122629