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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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On the existence of central sequences in subfactors
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by Dietmar H. Bisch PDF
Trans. Amer. Math. Soc. 321 (1990), 117-128 Request permission

Abstract:

We prove a relative version of [Co1, Theorem 2.1] for a pair of type ${\text {I}}{{\text {I}}_1}$-factors $N \subset M$. This gives a list of necessary and sufficient conditions for the existence of nontrivial central sequences of $M$ contained in the subfactor $N$. As an immediate application we obtain a result by Bédos [Be, Theorem A], showing that if $N$ has property $\Gamma$ and $G$ is an amenable group acting freely on $N$ via some action $\sigma$, then the crossed product $N{ \times _\sigma }G$ has property $\Gamma$. We also include a proof of a relative Mc Duff-type theorem (see [McD, Theorems $1$, $2$ and $3$]), which gives necessary and sufficient conditions implying that the pair $N \subset M$ is stable.
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Additional Information
  • © Copyright 1990 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 321 (1990), 117-128
  • MSC: Primary 46L35
  • DOI: https://doi.org/10.1090/S0002-9947-1990-1005075-5
  • MathSciNet review: 1005075