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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Spectrum of a compact weighted composition operator


Author: Gajath Gunatillake
Journal: Proc. Amer. Math. Soc. 135 (2007), 461-467
MSC (2000): Primary 47B32
Published electronically: September 11, 2006
MathSciNet review: 2255292
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Abstract: For $ \psi$ analytic in the open unit disk and $ \varphi$ an analytic map from the unit disk into itself, the weighted composition operator $ C_{\psi,\varphi}$ is the operator on the weighted Hardy space $ H^{2}(\beta) $ given by $ (C_{\psi,\varphi}f)(z)=\psi(z)f(\varphi(z)).$ This paper discusses the spectrum of $ C_{\psi,\varphi}$ when it is compact on a certain class of weighted Hardy spaces and when the composition map $ \varphi$ has a fixed point inside the open unit disk.


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Additional Information

Gajath Gunatillake
Affiliation: Department of Mathematics and Statistics, American University of Sharjah, P. O. Box 26666, Sharjah, United Arab Emirates

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08497-8
PII: S 0002-9939(06)08497-8
Received by editor(s): February 3, 2005
Received by editor(s) in revised form: September 19, 2005
Published electronically: September 11, 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.