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november 2020 Complex symmetry of weighted composition operators on the space $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$
Aastha Malhotra, Anuradha Gupta
Bull. Belg. Math. Soc. Simon Stevin 27(4): 595-607 (november 2020). DOI: 10.36045/j.bbms.200316

Abstract

We investigate the complex symmetric structure of the weighted composition operator $W_{\psi,\phi}$ on the subspace $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$ of the Hardy space $\mathcal{H}^2(\mathbb{D})$ of codimension one. We provide characterizations of symbols $\phi$ and $\psi$ such that $W_{\psi,\phi}$ is complex symmetric with respect to a special conjugation. In addition, we discuss isometric properties of the complex symmetric operator $W_{\psi,\phi}$ on $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$.

Citation

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Aastha Malhotra. Anuradha Gupta. "Complex symmetry of weighted composition operators on the space $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 595 - 607, november 2020. https://doi.org/10.36045/j.bbms.200316

Information

Published: november 2020
First available in Project Euclid: 20 November 2020

MathSciNet: MR4177396
Digital Object Identifier: 10.36045/j.bbms.200316

Subjects:
Primary: 47B33 , 47B38

Keywords: Complex symmetric , Composition operator , conjugation

Rights: Copyright © 2020 The Belgian Mathematical Society

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Vol.27 • No. 4 • november 2020
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