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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 $ L$ and direct integral decompositions of $ W-\ast$algebras


Author: Paul Willig
Journal: Proc. Amer. Math. Soc. 30 (1971), 87-91
MSC: Primary 46.65
MathSciNet review: 0285920
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Abstract: If $ \mathcal{A}$ is a type $ \mathrm{II}_\infty W$-$ *$ algebra on separable Hilbert space $ H,\mathcal{A}$ is spatially isomorphic to $ \mathfrak{B} \otimes B(K),\mathfrak{B}$ of type $ \mathrm{II}_1$, K a separable Hilbert space. If $ \mathcal{A}(\lambda )$ are the factors in the direct integral decomposition of $ \mathcal{A}$, the set $ \mathfrak{L} = \{ \lambda \vert\mathcal{A}(\lambda )$ has property L} is $ \mu $-measurable, and $ \mathcal{A}$ has property L iff $ \mu (\Lambda - \mathfrak{L}) = 0$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0285920-5
PII: S 0002-9939(1971)0285920-5
Keywords: $ W{{\text{ - }}^ \ast }$ algebra, separable Hilbert space, direct integral decomposition, property L, central sequence
Article copyright: © Copyright 1971 American Mathematical Society