Compact differences of composition operators on large 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.