Property $L$ and direct integral decompositions of $W-\ast$algebras
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- by Paul Willig PDF
- Proc. Amer. Math. Soc. 30 (1971), 87-91 Request permission
Abstract:
If $\mathcal {A}$ is a type $\mathrm {II}_\infty W\text {-}*$ 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 $\mathfrak {L} = \{ \lambda |\mathcal {A}(\lambda )$ has property L} is $\mu$-measurable, and $\mathcal {A}$ has property L iff $\mu (\Lambda - \mathfrak {L}) = 0$.References
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Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 30 (1971), 87-91
- MSC: Primary 46.65
- DOI: https://doi.org/10.1090/S0002-9939-1971-0285920-5
- MathSciNet review: 0285920