Weighted ergodic theorem for contractions of Orlicz-Kantorovich lattice $L_{M}(\hat{\nabla},\hat{\mu}$

TL;DR

This paper proves a weighted ergodic theorem for positive contractions on Orlicz-Kantorovich lattices using measurable bundles of Banach-Kantorovich lattices, extending ergodic theory in this setting.

Contribution

It introduces a Besocovich weighted ergodic theorem for contractions on Orlicz-Kantorovich spaces, utilizing measurable bundle methods for the first time in this context.

Findings

Establishment of a weighted ergodic theorem for positive contractions.

Application of measurable bundle techniques to Orlicz-Kantorovich lattices.

Extension of ergodic theory to new functional analytic settings.

Abstract

In the present paper we prove Besocovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.