Some characterizations of ergodicity in Riesz spaces

Abstract

AbstractIn 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 L1(T) and operates as an isometry on Lp (T) spaces.Mathematics Subject Classification (2020): 47B6037A3047A3560A10Key words: Riesz spacesconditional expectationergodicityRiesz homomorphism