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Proceedings of the American Mathematical Society

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Property $ {\rm L}$ and asymptotic abelianness for von Neumann algebras of type $ {\rm I}$


Author: Shinzō Kawamura
Journal: Proc. Amer. Math. Soc. 84 (1982), 365-369
MSC: Primary 46L10; Secondary 46L50
DOI: https://doi.org/10.1090/S0002-9939-1982-0640232-X
MathSciNet review: 640232
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Abstract: We prove a correct assertion on Property L for von Neumann algebras of type I: a type I von Neumann algebra $ M$ on a separable Hilbert space has Property L if and only if $ M$ contains no minimal projection. Furthermore, a correct proof of an assertion on asymptotic abelianness for von Neumann algebras of type I is also given.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0640232-X
Keywords: von Neumann algebra, type I, Property L, minimal projection, asymptotic abelianness
Article copyright: © Copyright 1982 American Mathematical Society