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

Kosaki, Hideki

doi:10.1090/S0002-9939-1983-0681835-7

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

Proc. Amer. Math. Soc. 87 (1983), 283-288

DOI: https://doi.org/10.1090/S0002-9939-1983-0681835-7

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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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