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Composition operators with maximal norm on weighted Bergman spaces
Author(s):
Brent
J.
Carswell;
Christopher
Hammond
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2599-2605.
MSC (2000):
Primary 47B33
Posted:
February 17, 2006
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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:
10.1090/S0002-9939-06-08271-2
PII:
S 0002-9939(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
Posted:
February 17, 2006
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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