A remark on amenable von Neumann subalgebras in a tracial free product
Abstract
Let M=M1*M2 be a nontrivial tracial free product of finite von Neumann algebras. We prove that any amenable subalgebra of M that has a diffuse intersection with M1 is in fact contained in M1. This has been proved by C. Houdayer under more general circumstances.
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