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**Essentially hyponormal weighted composition operators on the Hardy and weighted Bergman spaces.**
*(English)*
Zbl 07104710

Summary: Let \(\varphi\) be an analytic self-map of the open unit disk \(\mathbb{D}\) and let \(\psi\) be an analytic function on \(\mathbb{D}\) such that the weighted composition operator \(C_{\psi,\varphi}\) defined by \(C_{\psi,\varphi}(f)=\psi f\circ\varphi\) is bounded on the Hardy and weighted Bergman spaces. We characterize those weighted composition operators \(C_{\psi,\varphi}\) on \(H^2\) and \(A_{\alpha}^2\) that are essentially hypo-normal, when \(\varphi\) is a linear-fractional non-automorphism.

### Keywords:

Hardy space; weighted Bergman spaces; weighted composition operator; hyponormal; essentially hyponormal
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\textit{M. Fatehi}, Rocky Mt. J. Math. 49, No. 4, 1129--1142 (2019; Zbl 07104710)

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