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Topological Structure of the Set of Weighted Composition Operators on Weighted Bergman Spaces of Infinite Order |
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| Authors: | José Bonet Mikael Lindström Elke Wolf |
| Institution: | 1. Instituto Universitario de Matematica Pura y Aplicada, IUMPA-UPV, Edificio ID15(8E), Cubo F, Cuarta Planta, Universidad Politécnica de Valencia, E-46022, Valencia, Spain 2. Department of Mathematical Sciences, University of Oulu, P.O. Box 3000, FIN-90014, Oulu, Finland 3. Institute of Mathematics, University of Paderborn, D-33095, Paderborn, Germany |
| Abstract: | We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H∞) and L(H∞v) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated. |
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