Uniform ergodic theorems for Markov operators on C(X) (Q5896247)

The main result of this article is the following theorem. A Markov operator T on C(X) space is quasi-compact provided the following three conditions are fulfilled: (i) the adjoint operator T' is strongly ergodic, that is the averages \(T'\!_ n=n^{-1}\sum^{n-1}_{i=0}(T')^ i\) converge in the strong operator topology, (ii) the subspce \(\{f\in X': T'f = f\}\) is separable, (iii) any T-invariant probability measure has non-meager support. There are some more interesting results and examples.