Cesaro convergence of spherical averages for measure-preserving actions of Markov semigroups and groups

Cesaro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in $L^p$, $1\le p<\mathrm{\infty }$, and pointwise convergence for functions in $L^{\mathrm{\infty }}$. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Cesaro convergence of spherical averages with respect to any symmetric set of generators.