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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On hyperfinite $ W-\sp{\ast} $ algebras


Author: Paul Willig
Journal: Proc. Amer. Math. Soc. 40 (1973), 120-122
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9939-1973-0328618-9
MathSciNet review: 0328618
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Abstract: If $ \mathcal{A}$ is a $ W{ - ^\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{J} = \{ \lambda \vert\mathcal{A}(\lambda )$ is hyperfinite} is $ \mu $-measurable, and $ \mathcal{A}$ is hyperfinite if and only if $ \mathcal{A}(\lambda )$ is hyperfinite $ \mu $-a.e.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0328618-9
Keywords: Hyperfinite, $ W$-$ \ast $ algebra, direct integral decomposition
Article copyright: © Copyright 1973 American Mathematical Society