The Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras
Summary: We prove an analogue of \textit{S. Sakai}'s [Bull. Am. Math. Soc. 71, 149--151 (1965; Zbl 0132.10803)] Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras. Following \textit{N. Takesaki} [Tomita's theory of modular Hilbert algebras and its application. Berlin etc.: Springer-Verlag (1970; Zbl 0193.42502)] we characterize the Radon-Nikodym derivatives by analytic extensions of modular automorphism groups. Finally, we relate the facial structure in \(L^p\)-spaces of \(W^*\)-algebras to \textit{A. Connes}' [Ann. Ec. Norm. Sup. 6, 133--252 (1973; Zbl 0274.46050)] unitary Radon-Nikodym cocycles.
Radon-Nikodym theorem for \(L^p\)-spaces of \(W^*\)-algebras
analytic extensions of modular automorphism groups
scientific article; zbMATH DE number 4054344