The essential norm of a composition operator on the minimal Mobius invariant space

TL;DR

This paper derives a formula for the essential norm of composition operators on the minimal Mobius invariant space, providing bounds and calculations related to boundary behavior and finite Blaschke products.

Contribution

It introduces a new formula for the essential norm of composition operators on the minimal Mobius invariant space and analyzes their behavior near the boundary.

Findings

Essential norm of non-compact operators is at least 1.

Lower bounds depend on boundary behavior of the symbol.

Order of magnitude for operators induced by finite Blaschke products is established.

Abstract

We derive a formula for the essential norm of a composition operator on the minimal Mobius invariant space of analytic functions. As an application, we show that the essential norm of a non-compact composition operator is at least 1. We also obtain lower bounds depending on the behavior of the symbol near the boundary, and calculate the order of magnitude of the essential norm of composition operators induced by finite Blaschke products.