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Kernel-induced distance and its applications to Composition operators on Large Bergman spaces (2407.14724v1)

Published 20 Jul 2024 in math.FA

Abstract: In this paper, we obtain a complete characterization for the compact difference of two composition operators acting on Bergman spaces with a rapidly decreasing weight $\omega=e{-\eta}$, $\Delta\eta>0$. In addition, we provide simple inducing maps which support our main result. We also study the topological path connected component of the space of all bounded composition operators on $A2(\omega)$ endowed with the Hilbert-Schmidt norm topology.

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