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On the existence of central sequences in subfactors


Author: Dietmar H. Bisch
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1990-1005075-5
Article copyright: © Copyright 1990 American Mathematical Society

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