Normal complex symmetric weighted composition operators on the Hardy space

Abstract

In this paper, we investigate the normal weighed composition operators $W_{\psi ,\phi }$ which is $\mathcal{J}-$symmetric, ${\mathcal{C}}_1-$symmetric and ${\mathcal{C}}_2-$symmetric on the Hardy space $H^2(\mathbb{D})$ respectively. Firstly, equivalent conditions of the normality of ${\mathcal{C}}_1-$symmetric and ${\mathcal{C}}_2-$symmetric weighted composition operators on $H^2(\mathbb{D})$ is given. Furthermore, the normal $\mathcal{J}-$symmetric, ${\mathcal{C}}_1-$symmetric and ${\mathcal{C}}_2-$symmetric weighted composition operators on $H^2(\mathbb{D})$ when $\phi$ has an interior fixed point, $\phi$ is of hyperbolic type or parabolic type are respectively investigated.

18 pages

References in corpus (1)

• Self-adjoint, unitary, and normal weighted composition operators in several variables