LAUSR

In this paper, we establish a non-commutative analogue of Calderón’s transference principle, which allows us to deduce the non-commutative maximal ergodic inequalities from the special case—operator-valued maximal inequalities. As applications, we deduce the non-commutative Stein–Calderón maximal ergodic inequality and the dimension-free estimates of the non-commutative Wiener maximal ergodic inequality over Euclidean spaces. We also show the corresponding individual ergodic theorems. To show Wiener’s pointwise ergodic theorem, following a somewhat standard way we construct a dense subset on which pointwise convergence holds. To show Jones’ pointwise ergodic theorem, we use again the transference principle together with the Littlewood–Paley method, which is different from Jones’ original variational method that is still unavailable in the non-commutative setting.