Digital Commons @ Connecticut College

Title

Composition operators with maximal norm on weighted Bergman spaces

Authors

Brent J. Carswell, Allegheny CollegeFollow
Christopher Hammond, Connecticut CollegeFollow

Document Type

Article

Publication Date

9-2006

Comments

First published in Proceedings of the American Mathematical Society in 134 (2006) no. 9

© 2006 American Mathematical Society

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

http://dx.doi.org/10.1090/S0002-9939-06-08271-2

Abstract

We prove that any composition operator with maximal norm on one of the weighted Bergman spaces 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 H², where every inner function induces a composition operator with maximal norm.

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Recommended Citation

Carswell, B. J., and C. Hammond, 2006: Composition operators with maximal norm on weighted Bergman spaces. Proceedings of the American Mathematical Society, 134, 2599-2605.