Coposinormal Weighted composition operators on $H^{2}(\mathbb{D})$

Abstract

In this paper, we study  coposinormal  composition operators and posinormal weighted  composition operators on the Hardy space $H^{2}(\mathbb{D})$. We show that if $W_{\psi,\varphi}$ is coposinormal on $H^{2}(\mathbb{D})$, then $\psi$ never vanishes on $\mathbb{D}$ also we prove that  $\varphi$ is univalent. Moreover, we study the commutant of a coposinormal weighted composition operator.