Hariharan G | Searcharxiv

arXiv2026

Non-Commutative Wiener-Wintner theorem for amenable group actions

Let $G$ be a locally compact, second countable, amenable group acting on a finite von Neumann algebra $(\mathcal{M},τ)$ 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.

math.OA↗

arXiv2025

Non-Commutative Maximal Inequalities for State-Preserving Actions of amenable groups

In this article, we establish maximal inequalities and deduce ergodic theorems for state-preserving actions of amenable, locally compact, second-countable groups on tracial non-commutative $L^1$-spaces. As a further consequence, in combination with the Neveu decomposition, we obtain a stochastic ergodic theorem for amenable group actions.

math.OA↗