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Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
Author(s):
Michael
T.
Jury
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3669-3675.
MSC (2000):
Primary 47B33;
Secondary 47B32, 46E22
Posted:
August 15, 2007
MathSciNet review:
2336583
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Additional information
Abstract:
We prove that the norm of a weighted composition operator on the Hardy space  of the disk is controlled by the norm of the weight function in the de Branges-Rovnyak space associated to the symbol of the composition operator. As a corollary we obtain a new proof of the boundedness of composition operators on  and recover the standard upper bound for the norm. Similar arguments apply to weighted Bergman spaces. We also show that the positivity of a generalized de Branges-Rovnyak kernel is sufficient for the boundedness of a given composition operator on the standard function spaces on the unit ball.
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Additional Information:
Michael
T.
Jury
Affiliation:
Department of Mathematics, University of Florida, Gainesville, Florida 32603
Email:
mjury@math.ufl.edu
DOI:
10.1090/S0002-9939-07-08931-9
PII:
S 0002-9939(07)08931-9
Received by editor(s):
July 27, 2006
Received by editor(s) in revised form:
September 19, 2006
Posted:
August 15, 2007
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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