Model Theory and the mean ergodic theorem for abelian unitary actions

Abstract

We explore connections between von Neumann's mean ergodic theorem and concepts of model theory. As an application we present a proof Wiener's generalization of von Neumann's result in which the group acting on the Hilbert space $\mathcal{H}$ is any abelian group of unitary transformations of $\mathcal{H}$.