Reproducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators
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- by Michael T. Jury PDF
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Abstract:
We prove that the norm of a weighted composition operator on the Hardy space $H^2$ 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 $H^2$ 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.References
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Additional Information
- Michael T. Jury
- Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32603
- MR Author ID: 742791
- Email: mjury@math.ufl.edu
- Received by editor(s): July 27, 2006
- Received by editor(s) in revised form: September 19, 2006
- Published electronically: August 15, 2007
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3669-3675
- MSC (2000): Primary 47B33; Secondary 47B32, 46E22
- DOI: https://doi.org/10.1090/S0002-9939-07-08931-9
- MathSciNet review: 2336583