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

Lian Hu; Songxiao Li; Rong Yang

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

Complex Variables 2022-04-18 v2 Functional Analysis

Authors: Lian Hu , Songxiao Li , Rong Yang

Abstract

A bounded linear operator $T$ on a separable complex Hilbert space $H$ is called $C$ -normal if there is a conjugation $C$ on $H$ 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

composition operators operator theory on hilbert spaces operator theory

Cite

@article{arxiv.2202.13909,
  title  = {$C$-normal weighted composition operators on $H^2$},
  author = {Lian Hu and Songxiao Li and Rong Yang},
  journal= {arXiv preprint arXiv:2202.13909},
  year   = {2022}
}

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