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 | References | Similar Articles | Additional Information

Abstract: We prove a relative version of [Co1, Theorem 2.1] for a pair of type -factors . This gives a list of necessary and sufficient conditions for the existence of nontrivial central sequences of contained in the subfactor . As an immediate application we obtain a result by Bédos [Be, Theorem A], showing that if has property and is an amenable group acting freely on via some action , then the crossed product has property . We also include a proof of a relative Mc Duff-type theorem (see [McD, Theorems , and ]), which gives necessary and sufficient conditions implying that the pair is stable.

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DOI:
https://doi.org/10.1090/S0002-9947-1990-1005075-5

Article copyright:
© Copyright 1990
American Mathematical Society