On the pointwise entangled ergodic theorem

We present some twisted compactness conditions for almost everywhere convergence of one-parameter entangled ergodic averages of Dunford-Schwartz operators T0,…,Ta on a Borel probability space of the form1N∑n=1NTanAa−1Ta−1nAa−1⋅…⋅A0T0nf for f∈Lp(X,μ), p≥1. We also discuss examples and present a continuous version of the result.