The Radon-Nikodym theorem for <i>L^p</i>-spaces of <i>W</i>*-algebras

Abstract

We prove an analogue of Sakai's [15] Radon-Nikodym theorem for Lp-spaces of W*-algebras. Following Takesaki [20] we characterize the Radon-Nikodyru derivatives by analytic extensions of modular automorphism groups. Finally we relate the facial structure in Lp-spaces of W*-algebras to Connes5 [2] unitary Radon-Nikodym cocycles.