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

Free product von Neumann algebras of type $ {\rm III}$


Author: Lance Barnett
Journal: Proc. Amer. Math. Soc. 123 (1995), 543-553
MSC: Primary 46L10; Secondary 46L35
MathSciNet review: 1224611
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Abstract: In this paper we will show that most free products of von Neumann algebras with respect to nontracial states produce type $ {\text{III}_\lambda }$ factors $ (\lambda \ne 0)$. In addition, for all such $ \lambda $, examples can be obtained with the component algebras being finite dimensional. Finally, conditions will be given to ensure that these free products will be full factors.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1224611-7
PII: S 0002-9939(1995)1224611-7
Article copyright: © Copyright 1995 American Mathematical Society