Commutator criteria for strong mixing II. More general and simpler

Abstract

We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong mixing property of discrete flows $\{U^N{\}}_{N\in \mathbb{Z}}$ and continuous flows $\{{\mathrm{e}}^{-itH}{\}}_{t\in \mathbb{R}}$ induced by unitary operators $U$ and self-adjoint operators $H$ in a Hilbert space. As an application, we present a short alternative proof (not using convolutions) of the strong mixing property of the left regular representation of $\sigma$-compact locally compact groups.

8 pages