Mean ergodic composition operators on spaces of holomorphic functions on a Banach space

TL;DR

This paper investigates the properties of mean ergodic composition operators on various spaces of holomorphic functions defined on the unit ball of Banach and Hilbert spaces, providing multiple examples across different function spaces.

Contribution

It introduces a comprehensive analysis of mean ergodic composition operators on infinite-dimensional holomorphic function spaces, with new examples illustrating diverse behaviors.

Findings

Characterization of mean ergodic composition operators in different function spaces

Examples demonstrating various ergodic properties

Insights into the structure of holomorphic function spaces on Banach and Hilbert spaces

Abstract

We study mean ergodic composition operators on infinite dimensional spaces of holomorphic functions of different types when defined on the unit ball of a Banach or a Hilbert space: that of all holomorphic functions, that of holomorphic functions of bounded type and that of bounded holomorphic functions. Several examples in the different settings are given.