Geodesic
Takesaki's duality theorem and continuous decomposition for real factors of type~III
Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 827-845

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Let $R$ be a real von Neumann algebra, and let $\mathcal U(R)$ be the least von Neumann algebra generated by $R$. We consider crossed products of $\mathcal U(R)$ and strongly continuous actions of commutative locally compact groups of $^*$-automorphisms of $\mathcal U(R)$. We study the real structure in the von Neumann algebras dual to $\mathcal U(R)$ (in the sense of the Takesaki duality for crossed products). We obtain a theorem on the continuous decomposition of real factors of type III. 
@article{IM2_2000_64_4_a6,
     author = {Sh. M. Usmanov},
     title = {Takesaki's duality theorem and continuous decomposition for real factors of {type~III}},
     journal = {Izvestiya. Mathematics },
     pages = {827--845},
     publisher = {mathdoc},
     volume = {64},
     number = {4},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a6/}
}
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Sh. M. Usmanov. Takesaki's duality theorem and continuous decomposition for real factors of type~III. Izvestiya. Mathematics , Tome 64 (2000) no. 4, pp. 827-845. http://geodesic.mathdoc.fr/item/IM2_2000_64_4_a6/