Author

Liang Wang

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Preprint Oct 2026

Noncommutative maximal inequalities for polynomial ergodic averages

We prove a noncommutative maximal ergodic inequality for averages along polynomial sequences. Let $\gamma$ be a trace-preserving automorphism of a semifinite von Neumann algebra $(\mathcal N,\tau)$. We show that the associated polynomial averages \begin{equation*} A_Nf:=\frac1N\sum_{n=1}^N\gamma^{P(n)}(f), \qquad N\in\...

Gui-Xiang Hong, Wen-Bo Li, É. Ricard et al. · 0 citations

Preprint Aug 2026

Pointwise convergence of noncommutative ergodic averages along the primes

Let $\mathcal N$ be a von Neumann algebra equipped with a normal faithful semifinite trace, and let $\gamma$ be a trace-preserving automorphism of $\mathcal N$. We consider the ergodic averages along the prime numbers \[ A_N(x) := \frac1{|P_N|} \sum_{q\in P_N}\gamma^q(x), \qquad P_N:=\{q\leq N:q\ \text{is prime}\}. \]...

Guixiang Hong, Liang Wang · 1 citation