Ozawa's class for locally compact groups and unique prime factorization of group von Neumann algebras

We study class for locally compact groups. We characterize locally compact groups in this class as groups having an amenable action on a boundary that is small at infinity, generalizing a theorem of Ozawa. Using this characterization, we provide new examples of groups in class and prove a unique prime factorization theorem for group von Neumann algebras of products of locally compact groups in this class. We also prove that class is a measure equivalence invariant.status: Published onlin