Weighted ergodic theorems for Banach-Kantorovich lattice $L_{p}(\hat{\nabla},\hat{\mu})$

TL;DR

This paper establishes weighted ergodic theorems for positive contractions on Banach-Kantorovich lattice spaces, utilizing measurable bundle methods to extend classical ergodic results to this setting.

Contribution

It introduces weighted ergodic theorems for Banach-Kantorovich lattices using measurable bundle techniques, advancing the understanding of ergodic behavior in these spaces.

Findings

Proved weighted ergodic theorems for positive contractions.

Extended classical ergodic results to Banach-Kantorovich lattices.

Developed methods using measurable bundles of Banach-Kantorovich lattices.

Abstract

In the present paper we prove weighted ergodic theorems and multiparameter weighted ergodic theorems for positive contractions acting on $L_p(\hat{\nabla},\hat{\mu})$. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.