Some characterizations of ergodicity in Riesz spaces

2023/12/15 by Youssef Azouzi, Azouzi, Youssef, Marwa Masmoudi +1 · 1 citation
Economics, Econometrics and Finance · Mathematics · #46A40 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2312.12454

openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 from 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 the natural domain of T and operates as an isometry on L^p(T) spaces.

Cited by

• Strong completeness of Lp-type vector lattices

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