A remark on amenable von Neumann subalgebras in a tracial free product (1501.06373v2)

Abstract: Let $M=M_1*M_2$ 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 $M_1$ is in fact contained in $M_1$. This has been proved by C. Houdayer under more general circumstances.