On the uniqueness of the injective III1 factor

U. Haagerup

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Resumé

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∞. 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.
OriginalsprogEngelsk
TidsskriftDocumenta Mathematica
Vol/bind21
Udgave nummer2016
Sider (fra-til)1193-1226
ISSN1431-0635
StatusUdgivet - 2016

Citer dette

Haagerup, U. (2016). On the uniqueness of the injective III1 factor. Documenta Mathematica, 21(2016), 1193-1226.
Haagerup, U. / On the uniqueness of the injective III1 factor. I: Documenta Mathematica. 2016 ; Bind 21, Nr. 2016. s. 1193-1226.
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Haagerup, U 2016, 'On the uniqueness of the injective III1 factor', Documenta Mathematica, bind 21, nr. 2016, s. 1193-1226.

On the uniqueness of the injective III1 factor. / Haagerup, U.

I: Documenta Mathematica, Bind 21, Nr. 2016, 2016, s. 1193-1226.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

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AB - 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∞. 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.

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