Continuous Decomposition of Real von Neumann Algebras of Type III

Abstract

Let $\Re$ be a real von Neumann algebra. We consider Takesaki’s duality for enveloping von Neumann algebra $U(\Re ) = \Re + i\Re$ and the action of modular automorphism σ ^φ for α-invariant weight on $U(\Re )$, where α is an involutory *-antiautomorphisin of $U(\Re )$, generating $\Re$. We obtain the theorem of continuous decomposition of real type III factor into the crossed product of real von Neumann of type II_∞, by one-parameter group of automorphisms.