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A Radon-Nikodým theorem for natural cones associated with von Neumann algebras. II


Author: Hideki Kosaki
Journal: Proc. Amer. Math. Soc. 87 (1983), 283-288
MSC: Primary 46L50
DOI: https://doi.org/10.1090/S0002-9939-1983-0681835-7
MathSciNet review: 681835
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Abstract: A natural cone associated with a ($ \sigma $-finite) von Neumann algebra is considered. Let $ {\xi _0}$ be a cyclic and separating vector in the cone. For each vector $ \xi $ in the cone, there always exists a positive selfadjoint operator $ t$ affiliated with the algebra satisfying $ \xi = tJtJ{\xi _0}$. Certain uniqueness results on $ t$ for a given $ \xi $ are also obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1983-0681835-7
Article copyright: © Copyright 1983 American Mathematical Society

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