Essential Normality of automorphic composition operators
Abstract
We first characterize those composition operators that are essentially normal on the weighted Bergman space A2s(D) for any real s>-1, where induced symbols are automorphisms of the unit disk D. Using the same technique, we investigate the automorphic composition operators on the Hardy space H2(BN) and the weighted Bergman spaces A2s(BN) (s>-1). Furthermore, we give some composition operators induced by linear fractional self-maps of the unit ball BN that are not essentially normal.
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