Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\) (Q1093143)
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scientific article; zbMATH DE number 4021935
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\) |
scientific article; zbMATH DE number 4021935 |
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Connes' bicentralizer problem and uniqueness of the injective factor of type \(III_ 1\) (English)
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1987
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This paper completes the classification of injective factors, cf. \textit{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.
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classification of injective factors
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hyperfinite factor
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trivial bicentralizer
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Araki-Woods factor
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