Article

Integral Equations and Operator Theory

, Volume 62, Issue 3, pp 419-428

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

  • J. S. ManhasAffiliated withDepartment of Mathematics, College of Science, Sultan Qaboos University Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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