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Session 33. Spaces of analytic functions
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Compactness of a difference of composition operators on Dirichlet space |
Małgorzata Michalska, Maria Curie-Skłodowska University, Lublin, Poland
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The talk is based on the joint work with Andrzej M. Michalski
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Let \(\varphi\) be a self-map of the unit disk and let \(C_\varphi\) denote the composition operator with symbol \(\varphi\). We study compactness of the difference \(C_\varphi - C_\psi\) of two composition operators acting on the standard Dirichlet space \(\mathcal{D}\) and give a necessary condition in the case when \(\varphi\) and \(\psi\) are finitely valent. We also consider the special case when \(\varphi\) and \(\psi\) are linear-fractional self-maps.
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