Asymptotic abelianness of infinite factors
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- by M. S. Glaser PDF
- Trans. Amer. Math. Soc. 178 (1973), 41-56 Request permission
Abstract:
Studying Pukánszky’s type III factor, ${M_2}$, we show that it does not have the property of asymptotic abelianness and discuss how this property is related to property L. We also prove that there are no asymptotic abelian ${\text {II}_\infty }$ factors. The extension (by ampliation) of central sequences in a finite factor, N, to $M \otimes N$ is shown to be central. Also, we give two examples of the reduction (by equivalence) of a central sequence in $M \otimes N$ to a sequence in N. Finally, applying the definition of asymptotic abelianness of ${C^\ast }$-algebras to ${W^\ast }$-algebras leads to the conclusion that all factors satisfying this property are abelian.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 178 (1973), 41-56
- MSC: Primary 46L10
- DOI: https://doi.org/10.1090/S0002-9947-1973-0317062-0
- MathSciNet review: 0317062