Composition operators with maximal norm on weighted Bergman spaces

Carswell, Brent; Hammond, Christopher

doi:10.1090/S0002-9939-06-08271-2

Composition operators with maximal norm on weighted Bergman spaces

Authors: Brent J. Carswell and Christopher Hammond
Journal: Proc. Amer. Math. Soc. 134 (2006), 2599-2605
MSC (2000): Primary 47B33
DOI: https://doi.org/10.1090/S0002-9939-06-08271-2
Published electronically: February 17, 2006
MathSciNet review: 2213738
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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.

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