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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Free products of von Neumann algebras


Author: Wai Mee Ching
Journal: Trans. Amer. Math. Soc. 178 (1973), 147-163
MSC: Primary 46L10
DOI: https://doi.org/10.1090/S0002-9947-1973-0326405-3
MathSciNet review: 0326405
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Abstract: A new method of constructing factors of type $ {\text{II}_1}$, called free product, is introduced. It is a generalization of the group construction of factors of type $ {\text{II}_1}$ when the given group is a free product of two groups. If $ {A_1}$ and $ {A_2}$ are two von Neumann algebras with separating cyclic trace vectors and ortho-unitary bases, then the free product $ {A_1} \ast {A_2}$ of $ {A_1}$ and $ {A_2}$ is a factor of type $ {\text{II}_1}$ without property $ \Gamma $.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0326405-3
Keywords: von Neumann algebra, group construction factor of type $ {\text{II}_1}$, free product, property $ \Gamma $
Article copyright: © Copyright 1973 American Mathematical Society