Difference of Composition operators over Bergman spaces with exponential weights

Abstract

In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with weight ω = e −η , ∆η > 0 using the η-derived bounded distance of two analytic self maps inducing composition operators. In addition, we provide an example that supports our main result. We also study the topological structure of the space of all bounded composition operators on A 2 (ω) endowed with topologies which are induced by the operator norm and the Hilbert-Schmidt norm.