Difference of composition operators in the Polydiscs

TL;DR

This paper provides estimates for the essential norm of the difference between composition operators on bounded function spaces in the unit polydisc, and characterizes when this difference is compact.

Contribution

It introduces new estimates for the essential norm of composition operator differences and characterizes their compactness in the context of polydiscs.

Findings

Derived simple estimates for the essential norm of operator differences

Characterized compactness of the difference of composition operators

Applied results to bounded function spaces in polydiscs

Abstract

This paper gives some simple estimates of the essential norm for the difference of composition operators induced by $\phi$ and $\psi$ acting on bounded function space in the unit polydiscs $U^n$, where $\phi(z)$ and $\psi(z)$be holomorphic self-maps of $U^n$. As its applications, a characterization of compact difference is given for composition operators acting on the bounded function spaces.