We investigate pointwise convergence of entangled ergodic averages of Dunford–Schwartz operators on a Borel probability space. These averages take the form
where for some , and encodes the entanglement. We prove that, under some joint boundedness and twisted compactness conditions on the pairs , convergence holds almost everywhere for all . We also present an extension to polynomial powers in the case , in addition to a continuous version concerning Dunford–Schwartz -semigroups.
"Pointwise entangled ergodic theorems for Dunford–Schwartz operators." Banach J. Math. Anal. 12 (3) 634 - 650, July 2018. https://doi.org/10.1215/17358787-2017-0062