Non-Commutative Wiener-Wintner theorem for amenable group actions

Panchugopal Bikram; Sudipta Kundu; Hariharan G

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arXiv · 2606.30194

Non-Commutative Wiener-Wintner theorem for amenable group actions

Panchugopal Bikram·Sudipta Kundu·Hariharan G

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Abstract

Let $G$ be a locally compact, second countable, amenable group acting on a finite von Neumann algebra $(\mathcal{M},\tau)$ by trace-preserving automorphisms. In this article, we establish a Jacobs-de Leeuw-Glicksberg decomposition for this action, yielding a decomposition of $\mathcal{M}$ into its almost periodic and weakly mixing components. We also prove a noncommutative version of the van der Corput lemma. As an application, we establish a noncommutative Wiener-Wintner theorem for amenable group actions on finite von Neumann algebras.

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Panchugopal Bikram, Sudipta Kundu, Hariharan G. 2026-06-29. Non-Commutative Wiener-Wintner theorem for amenable group actions. https://arxiv.org/abs/2606.30194

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