Ergodic properties of convolution operators

Let $G$ be a locally compact group and $\mu$ be a measure on $G$. In this paper we find conditions for the convolution operators ${\lambda }_p(\mu )$, defined on $L^p(G)$ and given by convolution by $\mu$, to be mean ergodic and uniformly mean ergodic. The ergodic properties of the operators ${\lambda }_p(\mu )$ are related to the ergodic properties of the measure $\mu$ as well.