Mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$

TL;DR

This paper investigates the properties of mean ergodic composition operators on the space of bounded holomorphic functions on the unit ball in n-dimensional complex space, showing conditions for norm convergence and uniform mean ergodicity.

Contribution

It provides new results on the norm convergence and uniform mean ergodicity of composition operators on $H^ abla( extbf{B}_n)$ under certain assumptions.

Findings

Mean ergodic composition operators have norm convergent iterates.

Such operators are always uniformly mean ergodic.

Results depend on additional assumptions for convergence.

Abstract

In this paper, we study (uniformly) mean ergodic composition operators on $H^\infty(\mathbb{B}_n)$. Under some additional assumptions, it is shown that mean ergodic operators have norm convergent iterates in $H^\infty(\mathbb{B}_n)$, and that they are always uniformly mean ergodic.