The Essential Norm of a Composition Operator

Joel H. Shapiro


Annals of Mathematics 125 (1987), 375--404
Abstract: The essential norm of a composition operator on the Hardy space H^2 is expressed as the asymptotic upper bound of a quantity involving the Nevanlinna counting function of the inducing map. There results a complete function theoretic characterization of compact composition operators on H^2, with similar results holding for the standard-weighted Bergman spaces of the unit disc.
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