Ergodic properties of convolution operators

Abstract

Let G be a locally compact group and μ be a measure on G. In this paper we find conditions for the convolution operators λp(μ):Lp(G)→Lp(G) to be mean ergodic and uniformly mean ergodic. The ergodic properties of the operators λp(μ) are related to the ergodic properties of the measure μ as well.