On the Uniqueness of the Injective III_{1} 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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