Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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
Published electronically: February 17, 2006
MathSciNet review: 2213738
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B33

Retrieve articles in all journals with MSC (2000): 47B33

Additional Information

Brent J. Carswell
Affiliation: Department of Mathematics, Allegheny College, Meadville, Pennsylvania 16335

Christopher Hammond
Affiliation: Department of Mathematics and Computer Science, Connecticut College, New London, Connecticut 06320

Keywords: Composition operator, norm, essential norm
Received by editor(s): February 2, 2005
Received by editor(s) in revised form: March 21, 2005
Published electronically: February 17, 2006
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.