Runlian Xia

Ergodic Average Dominance for Unimodular Amenable Groups

In this talk, we show that ergodic averages of actions of second countable unimodular amenable groups along suitable F{\o}lner sequences are dominated by Ces\`aro means of a certain Markov operator, i.e. by ergodic averages of an integer action.

As a consequence, maximal and pointwise ergodic theorems for unimodular amenable group actions follow directly from the results for integer actions. Our combinatorial method applies to both commutative and noncommutative settings, putting them on an equal footing and avoiding technical difficulties associated with group complexity or noncommutativity.

Based on a joint work with Ujan Chakraborty and Joachim Zacharias.