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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Property $ P$ and direct integral decomposition of $ W\sp*$-algebras


Author: Paul Willig
Journal: Proc. Amer. Math. Soc. 29 (1971), 494-498
MSC: Primary 46.65
MathSciNet review: 0279600
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Abstract: If $ \mathcal{A}$ is a $ W{{\text{-}}^\ast}$ algebra on separable Hilbert space H, and if $ \mathcal{A}(\lambda )$ are the factors in the direct integral decomposition of $ \mathcal{A}$, then $ \mathcal{P} = \{ \lambda \vert\mathcal{A}(\lambda )$ has property P} is $ \mu $-measurable, and $ \mathcal{A}$, has property P iff $ \mathcal{A}(\lambda )$ has property P $ \mu $-a.e.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279600-X
PII: S 0002-9939(1971)0279600-X
Keywords: $ W{{\text{-}}^\ast}$ algebra, separable Hilbert space, direct integral decomposition, property P
Article copyright: © Copyright 1971 American Mathematical Society