@Article{Lo2020,
author = "Lo, Ching-on and Wai-keung Loh, Anthony",
title = "Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces",
journal = "Opuscula Math.",
year = "2020",
volume = "40",
number = "4",
pages = "495--507",
doi = "https://doi.org/10.7494/OpMath.2020.40.4.495",
url = "https://doi.org/10.7494/OpMath.2020.40.4.495",
abstract = "Let \(u\) and \(\varphi\) be two analytic functions on the unit disk \(\mathbb{D}\) such that \(\varphi(\mathbb{D}) \subset \mathbb{D}\). A weighted composition operator \(uC_{\varphi}\) induced by \(u\) and \(\varphi\) is defined on \(H^2\), the Hardy space of \(\mathbb{D}\), by \(uC_{\varphi}f := u \cdot f \circ \varphi\) for every \(f\) in \(H^2\). We obtain sufficient conditions for Hilbert-Schmidtness of \(uC_{\varphi}\) on \(H^2\) in terms of function-theoretic properties of \(u\) and \(\varphi\). Moreover, we characterize Hilbert-Schmidt difference of two weighted composition operators on \(H^2\).",
keywords = "weighted composition operators, Hardy spaces, compact operators, Hilbert-Schmidt operators",
issn = "1232-9274"
}