Annals of Mathematical Sciences and Applications

Volume 9 (2024)

Number 2

$C$-normal composition operators on $H^2$

Pages: 505 – 525

DOI: https://dx.doi.org/10.4310/AMSA.2024.v9.n2.a8

Authors

Lian Hu (Department of Mathematics, Shantou University, Shantou, China; Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China)

Songxiao Li (Department of Mathematics, Shantou University, Shantou, China)

Rong Yang (Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China)

Abstract

A bounded linear operator $T$ on a separable complex Hilbert space $\mathcal{H}$ is called $C$-normal if there is a conjugation $C$ on $\mathcal{H}$ such that $CT^\ast TC = TT^\ast$. Let $\varphi$ be a linear fractional self-map of $\mathbb{D}$. In this paper, we characterize the necessary and sufficient condition for the composition operator $C_\varphi$ and weighted composition operator $W_{\psi,\varphi}$ to be $C$-normal with some conjugations $C$ and a function $\psi$.

Keywords

hardy space, composition operator, weighted composition operator, $C$-normal

2010 Mathematics Subject Classification

Primary 30H10. Secondary 47B33.

Received 10 April 2023

Accepted 21 June 2023

Published 15 August 2024