Convergence theorems for weakly almost periodic Markov operators

Convergence theorems of both pointwise and uniform type are obtained on certain subsets for weakly almost perodic Markov operators onC(X). Several examples are considered to examine the sharpness of these results. Finally these results are used to obtain necessary and sufficient conditions for Blum-Hanson convergence of point transformations and sufficient conditions for Blum-Hanson convergence of Markov operators.