TY  - JOUR
ID  - Lo2020
LB  - Lo2020
AU  - Lo, Ching-on
AU  - Wai-keung Loh, Anthony
TI  - Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces
ST  - Hilbert-Schmidtness of weighted composition operators and their differences on Hardy spaces
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2020
VL  - 40
IS  - 4
SP  - 495
EP  - 507
DO  - https://doi.org/10.7494/OpMath.2020.40.4.495
UR  - https://doi.org/10.7494/OpMath.2020.40.4.495
AB  - 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 \(H^2\).
KW  - weighted composition operators
KW  - Hardy spaces
KW  - compact operators
KW  - Hilbert-Schmidt operators
SN  - 1232-9274
ER  -