Integral Equations and Operator Theory

, Volume 62, Issue 3, pp 419–428 | Cite as

Compact Differences of Weighted Composition Operators on Weighted Banach Spaces of Analytic Functions

Article

Abstract.

Let \(H_{\nu}^{\infty} (\mathbb{D})\) be the weighted Banach space of analytic functions with a topology generated by weighted sup-norm. In the present article, we investigate the analytic mappings \(\phi_{1},\phi_{2}:{\mathbb{D}} \rightarrow {\mathbb{D}}\) and \(\theta, \pi : {\mathbb{D}} \rightarrow {\mathbb{C}}\) which characterize the compactness of differences of two weighted composition operators \(W_{\phi_{1},\theta} -W_{\phi_{2},\pi}\) on the space \(H_{\nu}^{\infty}({\mathbb{D}}\). As a consequence we characterize the compactness of differences of composition operators on weighted Bloch spaces.

Mathematics Subject Classification (2000).

Primary 47B38, 47B37, 47B33, 47B07 Secondary 46E15, 46E10, 30H05 

Keywords.

Weighted composition operator weighted Banach space of analytic functions weighted sup-norm compact oerator 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Department of Mathematics, College of ScienceSultan Qaboos UniversityAl-KhodSultanate of Oman

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