Rocky Mountain Journal of Mathematics

Essentially hyponormal weighted composition operators on the Hardy and weighted Bergman spaces

Mahsa Fatehi

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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.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 4 (2019), 1129-1142.

Dates
First available in Project Euclid: 29 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1567044032

Digital Object Identifier
doi:10.1216/RMJ-2019-49-4-1129

Mathematical Reviews number (MathSciNet)
MR3998914

Zentralblatt MATH identifier
07104710

Subjects
Primary: 47B33: Composition operators
Secondary: 47B20: Subnormal operators, hyponormal operators, etc.

Keywords
Hardy space weighted Bergman spaces weighted composition operator hyponormal essentially hyponormal

Citation

Fatehi, Mahsa. Essentially hyponormal weighted composition operators on the Hardy and weighted Bergman spaces. Rocky Mountain J. Math. 49 (2019), no. 4, 1129--1142. doi:10.1216/RMJ-2019-49-4-1129. https://projecteuclid.org/euclid.rmjm/1567044032


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