Morgan O'Brien

Noncommutative extensions of an ergodic theorem of Breiman

Let $(\mathcal{M},\tau)$ be a tracial von Neumann algebra, $T:L_1(\mathcal{M},\tau)\to L_1(\mathcal{M},\tau)$ be induced by a normal $\tau$-preserving $*$-automorphism of $\mathcal{M}$, and $x\in L_1(\mathcal{M},\tau)$. We will prove the bilaterally almost uniform convergence of averages of the form $$\frac{1}{n}\sum_{...