, Volume 62, Issue 3, pp 419-428
Date: 08 Oct 2008

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

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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.