Some characterizations of ergodicity in Riesz spaces

Abstract

In the recent surge of papers on ergodic theory within Riesz spaces, this article contributes by introducing enhanced characterizations of ergodicity. Our work extends and strengthens prior results of both the authors and Homann, Kuo, and Watson. Specifically, we show that in a conditional expectation preserving system (E, T, S, e), S can be extended to L ¹(T) and operates as an isometry on L^p (T) spaces.