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1973 The Radon-Nikodym theorem for von neumann algebras
Gert K. Pedersen, Masamichi Takesaki
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Acta Math. 130: 53-87 (1973). DOI: 10.1007/BF02392262


Let ϕ be a faithful normal semi-finite weight on a von Neumann algebraM. For each normal semi-finite weight ϕ onM, invariant under the modular automorphism group Σ of ϕ, there is a unique self-adjoint positive operator h, affiliated with the sub-algebra of fixed-points for Σ, such that ϕ=ϕ(h·). Conversely, each such h determines a Σ-invariant normal semi-finite weight. An easy application of this non-commutative Radon-Nikodym theorem yields the result thatM is semi-finite if and only if Σ consists of inner automorphisms.

Funding Statement

Partially supported by NSF Grant # 28976 X.
Partially supported by NSF Grant # GP-28737

Version Information

This revised version was published online in November 2006 with corrections to the Cover Date.


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Gert K. Pedersen. Masamichi Takesaki. "The Radon-Nikodym theorem for von neumann algebras." Acta Math. 130 53 - 87, 1973.


Received: 2 May 1972; Published: 1973
First available in Project Euclid: 31 January 2017

zbMATH: 0262.46063
MathSciNet: MR412827
Digital Object Identifier: 10.1007/BF02392262

Rights: 1973 © Almqvist & Wiksell Informationsindustri AB

Vol.130 • 1973
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