A Radon-Nikodym theorem for von Neumann algebras

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dc.creatorVaes, Stefaan
dc.date1998-11-20
dc.date.accessioned2026-07-07T05:26:56Z
dc.date.available2026-07-07T05:26:56Z
dc.descriptionIn 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.
dc.description14 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/9811122
dc.identifierhttp://arxiv.org/abs/math/9811122
dc.identifierJournal of Operator Theory 46 (3) (2001), 477--489.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77743
dc.subjectOperator Algebras
dc.subjectFunctional Analysis
dc.subject46L50, 46L10
dc.titleA Radon-Nikodym theorem for von Neumann algebras
dc.typetext

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