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Compact weighted composition operators on the Hardy space

Author: Gajath Gunatillake
Journal: Proc. Amer. Math. Soc. 136 (2008), 2895-2899
MSC (2000): Primary 47B32
Published electronically: April 10, 2008
MathSciNet review: 2399056
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Abstract: A weighted composition operator $ C_{\psi,\varphi}$ takes an analytic map $ f$ on the open unit disk of the complex plane to the analytic map $ \psi f\circ \varphi$, where $ \varphi$ is an analytic map of the open unit disk into itself and $ \psi$ is an analytic map on the open unit disk. This paper studies how the compactness of $ C_{\psi,\varphi}$ depends on the interaction between the two maps $ \psi$ and $ \varphi$.

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Gajath Gunatillake
Affiliation: Department of Mathematics, American University of Sharjah, Sharjah, United Arab Emirates

Received by editor(s): August 1, 2006
Received by editor(s) in revised form: June 2, 2007
Published electronically: April 10, 2008
Additional Notes: The research for this paper was undertaken in partial fulfillment of the requirements for the author’s Ph.D. at Purdue University.
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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