A Radon-Nikodym theorem for von Neumann algebras

1998/11/20 by Stefaan Vaes · 2 citations
Mathematics · #math.OA #math.FA #msc:46L50 #msc:46L10

paper · pdf

published as Journal of Operator Theory 46 (3) (2001), 477--489. · 14 pages, LaTeX

arxiv created 1998/11/20 · arxiv updated 2009/11/30

Abstract

In this paper we present a generalization of the Radon-Nikodym theorem proved by Pedersen and Takesaki. Given a normal, semifinite and faithful (n.s.f.) weight ϕ on a von Neumann algebra M and a strictly positive operator δ, affiliated with M and satisfying a certain relative invariance property with respect to the modular automorphism group σ^ϕ of ϕ, with a strictly positive operator as the invariance factor, we construct the n.s.f. weight ϕ(δ^1/2 . δ^1/2). All the n.s.f. weights on M whose modular automorphisms commute with σ^ϕ are of this form, the invariance factor being affiliated with the centre of M. All the n.s.f. weights which are relatively invariant under σ^ϕ are of this form, the invariance factor being a scalar.

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• Reduced Density Matrix Functional Theory And A Reduced Formulation Of Density Functional Theory
• Analysis of the Plancherel weight and factoriality of the group von Neumann algebras of non-unimodular almost unimodular groups

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