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arXiv · 1510.00201

Commutator criteria for strong mixing II. More general and simpler

Serge Richard·Rafael Tiedra de Aldecoa
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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 $\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ 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.

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Serge Richard, Rafael Tiedra de Aldecoa. 2015-10-01. Commutator criteria for strong mixing II. More general and simpler. https://arxiv.org/abs/1510.00201

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