Amenable absorption in amalgamated free product von Neumann algebras

Abstract

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M=M_1{\ast }_B{M}_2$. 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 non normal conditional expectations.

8 pages. To appear in Kyoto J. Math

References in corpus (1)

• On a class of ${\mathrm{II}}_1$ factors with at most one Cartan subalgebra

Cited by in corpus (8)

• Fullness and Connes' $\mathbf{\tau }$ invariant of type III tensor product factors
• Structure of extensions of free Araki-Woods factors
• Asymptotic freeness in tracial ultraproducts
• Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras
• Unique prime factorization for infinite tensor product factors
• Thin II_1 factors with no Cartan subalgebras
• A random matrix approach to absorption in free products
• Maximal amenable MASAs of the free group factor of two generators arising from the free products of hyperfinite factors