Year: 2026
Type: preprint
Abstract: Let $G$ be a locally compact, second countable group admitting a Reiter sequence, and suppose that $G$ acts on a von Neumann algebra $\mathcal{M}$ equipped with a semifinite trace $τ$ via trace-preserving automorphisms. In this paper, we prove a maximal inequality for ergodic averages along such Reiter sequences. Our approach relies on approximating the Reiter sequence by a linear combination of characteristic functions of Følner sequences using the layer-cake representation. Furthermore, we establish the bilateral almost uniform convergence of these ergodic averages. As an application, we deduce a non-commutative Wiener-Wintner type theorem along Reiter sequences.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221835214