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 obtain a complete characterization of the compact differences of composition operators in Bergman spaces with weight of ω(z)=e−11−|z| using a newly defined Riemannian distance. Moreover, we discuss the compact differences of composition operators in Bergman spaces with general weights.