An Abel-maximal ergodic theorem for semi-groups

Abstract

The purpose of this paper is to prove a maximal ergodic theorem for Abel means of a strongly measurable semi-group ={T t ;t^0} of linear contractions on a complex Li-space satisfying | T t f | ^ c a.e. for any t > 0 and any integrable / with I /1 ^ c a.e. Applying the obtained maximal ergodic theorem, individual and dominated ergodic theorems for Abel means are also proved. These results extend results obtained by D. A. Edwards for sub-Markovian semi-groups.