Compact differences of composition operators on large weighted Bergman spaces

TL;DR

This paper characterizes the compact differences of composition operators on large weighted Bergman spaces using a new Riemannian distance, advancing understanding in a less-explored area of operator theory.

Contribution

It introduces a new Riemannian distance to characterize compact differences of composition operators on large weighted Bergman spaces, filling a gap in existing research.

Findings

Provided characterizations of compact differences of composition operators.

Established a sufficient condition for two operators to be in the same component.

Extended analysis to exponential type weighted Bergman spaces.

Abstract

While there have been extensive studies regarding the theory of composition operators in standard Bergman spaces, there have not been many results pertaining to large Bergman spaces due to a lack of useful tools. In this paper, we give the characterizations of the compact differences of composition operators in Bergman spaces with the exponential type weight using a newly defined Riemannian distance. Furthermore, we give a sufficient condition for the question when two composition operators lie in the same component.