On the Uniqueness of the Injective III1 Factor
We give a new proof of a theorem due to Alain Connes, that an injective factor $N$ of type III$1$ with separable predual and with trivial bicentralizer is isomorphic to the Araki--Woods type III$1$ factor $R\infty$. This, combined with the author's solution to the bicentralizer problem for injective III$1$ factors provides a new proof of the theorem that up to $*$-isomorphism, there exists a unique injective factor of type III$1$ on a separable Hilbert space.
2010 Mathematics Subject Classification: 46L36
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