Research Article

Some characterizations of ergodicity in Riesz spaces

Published in: Quaestiones Mathematicae
Volume 47 , issue 11 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 2319–2329
DOI: 10.2989/16073606.2024.2366410
Author(s): Youssef Azouzi Tunis-El Manar University, Tunisia, Marwa Masmoudi Tunis-El Manar University, Tunisia,
Keywords: 47B60, 37A30, 47A35, 60A10, Riesz spaces, conditional expectation, ergodicity, Riesz homomorphism,
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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 Lp (T) spaces.
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