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Composition operators with maximal norm on weighted Bergman spaces

Authors:	Brent J Carswell Christopher Hammond

Institution:	Department of Mathematics, Allegheny College, Meadville, Pennsylvania 16335 ; Department of Mathematics and Computer Science, Connecticut College, New London, Connecticut 06320

Abstract:	We prove that any composition operator with maximal norm on one of the weighted Bergman spaces $A^{2}_{\alpha}$ (in particular, on the space $A^{2}=A^{2}_{0}$ ) is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space $H^{2}$ , where every inner function induces a composition operator with maximal norm.

Keywords:	Composition operator norm essential norm

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