Amenable absorption in amalgamated free product von Neumann algebras

Abstract

We investigate the position of amenable subalgebras in arbitrary amalga- mated free product von Neumann algebras $M=M_1{*}_B{M}_2$. Our main result states that, under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$. The proof does not rely on Popa’s asymptotic orthogonality property but on the study of nonnormal conditional expectations.