Geodesic
On the uniqueness of the injective $\mathrm{III}_{1}$ factor
Documenta mathematica, Tome 21 (2016), pp. 1193-1226
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We give a new proof of a theorem due to Alain Connes, that an injective factor N of type III1​ with separable predual and with trivial bicentralizer is isomorphic to the Araki–Woods type III1​ factor R_infty. This, combined with the author's solution to the bicentralizer problem for injective III1​ factors provides a new proof of the theorem that up to ∗-isomorphism, there exists a unique injective factor of type III1​ on a separable Hilbert space.
DOI : 10.4171/dm/556
Classification : 46L36 
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     author = {Uffe Haagerup},
     title = {On the uniqueness of the injective $\mathrm{III}_{1}$ factor},
     journal = {Documenta mathematica},
     pages = {1193--1226},
     year = {2016},
     volume = {21},
     doi = {10.4171/dm/556},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/556/}
}
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Uffe Haagerup. On the uniqueness of the injective $\mathrm{III}_{1}$ factor. Documenta mathematica, Tome 21 (2016), pp. 1193-1226. doi: 10.4171/dm/556

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