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

Let be a real von Neumann algebra, and let be the least von Neumann algebra generated by . We consider crossed products of and strongly continuous actions of commutative locally compact groups of -automorphisms of . We study the real structure in the von Neumann algebras dual to (in the sense of the Takesaki duality for crossed products). We obtain a theorem on the continuous decomposition of real factors of type III.

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