Some applications of interpolating sequences for Banach spaces of analytic functions

TL;DR

This paper explores the use of interpolating sequences to establish new necessary and sufficient conditions for the mean ergodicity of composition operators on certain Banach spaces of analytic functions.

Contribution

It introduces novel criteria based on interpolating sequences for the mean ergodic behavior of composition operators on $H^(\u00d4)$ and related spaces.

Findings

New necessary and sufficient conditions for mean ergodicity.

Application of interpolating sequences to operator theory.

Enhanced understanding of composition operators on analytic function spaces.

Abstract

M. J. Beltr\'{a}n-Meneua et al. \cite{beltran1} and E. Jord\'{a} and A. Rodr\'{i}guez-Arenas \cite{jorda} characterized the (uniformly) mean ergodic composition operators on $H^\infty(\mathbb{D})$ and $H^\infty_\nu (\mathbb{D})$, respectively. In this paper, by using the interpolating sequences, we give other necessary and sufficient conditions for the (uniformly) mean ergodicity of composition operators on these spaces.