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Connes’ bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\). (English) Zbl 0628.46061
This paper completes the classification of injective factors, cf. A. Connes [Ann. Math., II. Ser. 104, 73-115 (1976; Zbl 0343.46042) and J. Oper. Theory 14, 189-211 (1985; Zbl 0597.46063)]. The author proves that any hyperfinite factor of type \(III_ 1\) has a trivial bicentralizer, and is, therefore isomorphic to the Araki-Woods factor \(R_{\infty}\). He also gives a characterization of \(III_ 1\)-factors with only trivial bicentralizers.
Reviewer: H.Schröder

MSC:
46L35 Classifications of \(C^*\)-algebras
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