The injective factors of type \(III_{\lambda}\), \(0<\lambda <1\)
type: Item
instance of: scholarly article
title: The injective factors of type \(III_{\lambda}\), \(0<\lambda <1\)
zbMATH Open document ID: 0685.46035
author: Uffe Haagerup
published in: Pacific Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: 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.
reviewed by: Joachim Cuntz
Mathematics Subject Classification ID: 46L35
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 4122629
zbMATH Keywords: injective factor of type \(III_{\lambda }\)
zbMATH Keywords: avoids the analysis of outer conjugacy classes of automorphisms of
zbMATH Keywords: factors
zbMATH Keywords: Hilbert \(W^*\)-bimodule
zbMATH Keywords: Dixmier's approximation theorem for \(III_{\lambda }\) factors
zbMATH Keywords: completely positive maps
zbMATH Keywords: avoids the analysis of outer conjugacy classes of automorphisms of factors
MaRDI profile type: Publication
full work available at URL: pjm.1989.137.265
OpenAlex ID: W1591384080
Wikidata QID: Q114045266
DOI: 10.2140/PJM.1989.137.265
description: scientific article; zbMATH DE number 4122629