The AMS website will be down for maintenance on May 23 between 6:00am - 8:00am EDT. For questions please contact AMS Customer Service at or (800) 321-4267 (U.S. & Canada), (401) 455-4000 (Worldwide).


Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46.65

Retrieve articles in all journals with MSC: 46.65

Additional Information

Keywords: $ W{{\text{ - }}^ \ast }$ algebra, separable Hilbert space, direct integral decomposition, property L, central sequence
Article copyright: © Copyright 1971 American Mathematical Society

American Mathematical Society