A note on the complex symmetric weighted composition operators over Hardy space

TL;DR

This paper characterizes complex symmetric weighted composition operators on the Hardy space, including subclasses like unitary, Hermitian, and normal, and shows that their weight functions are not always linear fractional.

Contribution

It provides a new characterization of algebraic weighted composition operators with degree up to two and clarifies the nature of their weight functions.

Findings

Includes subclasses such as unitary, Hermitian, and normal operators.

Shows weight functions are not necessarily linear fractional.

Provides a characterization for algebraic operators with degree ≤ 2.

Abstract

This paper provides a class of complex symmetric weighted composition operators on $H^2(\mathbb{D})$ to includes the unitary subclass, the Hermitian subclass and the normal subclass obtained by Bourdon and Noor. A characterization of algebraic weighted composition operator with degree no more than two is provided to illustrate that the weight function of a complex symmetric weighted composition operator is not necessarily linear fractional. \end{abstract}