Abstract
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.
Citation
Mahsa Fatehi. "Essentially hyponormal weighted composition operators on the Hardy and weighted Bergman spaces." Rocky Mountain J. Math. 49 (4) 1129 - 1142, 2019. https://doi.org/10.1216/RMJ-2019-49-4-1129
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