Takesaki's duality theorem and continuous decomposition for real factors of type III (Q2710701)

In 1973, M. Takesaki proved a duality theorem for actions of locally compact Abelian groups on von Neumann algebras and used it to construct a continuous decomposition of a \(\sigma\)-finite von Neumann algebra of type \(\text{III}\) into a crossed product of a von Neumann algebra of type \(\text{II}_{\infty}\) and a one-parameter group of star automorphisms. NEWLINENEWLINENEWLINEIn the present paper, the author studies real von Neumann algebras and obtains a continuous decomposition of real \(\sigma\)-finite factors of type \(\text{III}\).