Ergodic theorems for $L_1$--$L_\infty$ contractions in Banach--Kantorovich $L_p$-lattices

TL;DR

This paper extends ergodic theorems to $L_1$--$L_$ contractions within Banach--Kantorovich $L_p$-lattices linked to Maharam measures, broadening the scope of ergodic theory in functional analysis.

Contribution

It introduces ergodic theorems for contractions in Banach--Kantorovich lattices associated with Maharam measures, a novel setting in ergodic theory.

Findings

Established ergodic theorems for $L_1$--$L_$ contractions

Extended ergodic results to Banach--Kantorovich $L_p$-lattices

Applied to measures taking values in measurable functions

Abstract

We present versions of ergodic theorems for $L_1$--$L_\infty$ contractions in Banach--Kantorovich $L_p$-lattices associated with the Maharam measure taking values in the algebra of measurable functions.