Free product von Neumann algebras of type 𝐼𝐼𝐼

Barnett, Lance

doi:10.1090/S0002-9939-1995-1224611-7

Free product von Neumann algebras of type $\textrm {III}$
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Proc. Amer. Math. Soc. 123 (1995), 543-553 Request permission

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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