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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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