Journal of operator theory vol:46 issue:3 pages:477-489
In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki in . Given a normal, semifinite and faithful (n.s.f.) weight phi on a von Neumann algebra M and a strictly positive operator delta, affiliated with M and satisfying a certain relative invariance property with respect to the modular automorphisin group sigma(rho) of phi, with a strictly positive operator as the invariance factor, we construct the n.s.f. weight phi(delta1/2. delta1/2). All the n.s.f. weights on M whose modular automorphisins commute with sigma(rho) are of this form, the invariance factor being affiliated with the centre of M the n.s.f, weights which axe relatively invariant under sigma(phi) are of this form, the invariance factor being a scalar.