Guixiang Hong

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 \[ A_N(x) := \frac1{|P_N|} \sum_{q\in P_N}\gamma^q(x), \qquad P_N:=\{q\leq N:q\ \text{is prime}\}. \]...