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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Closedness of index values for subfactors


Authors: David Handelman and Hans Wenzl
Journal: Proc. Amer. Math. Soc. 101 (1987), 277-282
MSC: Primary 46L35
MathSciNet review: 902541
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Abstract: Let $ \left\{ {{A_i} \subset {B_i}} \right\}$ be a collection of inclusions of finite factors with the indices $ \left\{ {\left[ {{B_i}:{A_i}} \right]} \right\}$ bounded and each with trivial relative commutant. Then any $ {W^ * }$ ultraproduct yields an inclusion with trivial relative commutant whose index is the ultralimit of $ \left\{ {\left[ {{B_i}:{A_i}} \right]} \right\}$. In particular, the set of values of indices arising from pairs of factors with trivial relative commutant is a closed subset of $ {{\mathbf{R}}^ + }$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902541-0
PII: S 0002-9939(1987)0902541-0
Article copyright: © Copyright 1987 American Mathematical Society