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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: We prove that any composition operator with maximal norm on one of the weighted Bergman spaces (in particular, on the space
) 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
, where every inner function induces a composition operator with maximal norm.
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Additional Information
Brent J. Carswell
Affiliation:
Department of Mathematics, Allegheny College, Meadville, Pennsylvania 16335
Email:
brent.carswell@allegheny.edu
Christopher Hammond
Affiliation:
Department of Mathematics and Computer Science, Connecticut College, New London, Connecticut 06320
Email:
cnham@conncoll.edu
DOI:
https://doi.org/10.1090/S0002-9939-06-08271-2
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.