A quantitative multiparameter mean ergodic theorem

TL;DR

This paper applies proof mining techniques to derive a computable, uniform rate of metastability for the mean ergodic theorem involving multiple commuting linear contractive operators on uniformly convex Banach spaces.

Contribution

It introduces a novel proof mining approach to obtain explicit rates of metastability for the mean ergodic theorem in a multiparameter setting.

Findings

Derived a computable rate of metastability for the theorem

Extended the mean ergodic theorem to multiple operators

Provided uniform bounds applicable across classes of spaces

Abstract

We use techniques of proof mining to obtain a computable and uniform rate of metastability (in the sense of Tao) for the mean ergodic theorem for a finite number of commuting linear contractive operators on a uniformly convex Banach space.