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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 4, Pages 183–200 (Mi izv300)  

Takesaki's duality theorem and continuous decomposition for real factors of type III

Sh. M. Usmanov

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: 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.

DOI: https://doi.org/10.4213/im300

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English version:
Izvestiya: Mathematics, 2000, 64:4, 827–845

Bibliographic databases:

MSC: 46L35, 46L40, 46L55
Received: 28.01.1999

Citation: Sh. M. Usmanov, “Takesaki's duality theorem and continuous decomposition for real factors of type III”, Izv. RAN. Ser. Mat., 64:4 (2000), 183–200; Izv. Math., 64:4 (2000), 827–845

Citation in format AMSBIB
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  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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