Complex Symmetry and Normality of Toeplitz Composition Operators on the Hardy space

TL;DR

This paper explores the conditions for complex symmetry and normality of Toeplitz composition operators on the Hardy space, providing insights into their structural properties and classifications.

Contribution

It offers new characterizations of when Toeplitz composition operators are complex symmetric and normal on the Hardy space, expanding understanding of their operator-theoretic properties.

Findings

Identifies conditions for complex symmetry of Toeplitz composition operators.

Establishes criteria for normality of these operators.

Provides examples illustrating the theoretical results.

Abstract

In this paper, we investigate the conditions under which the Toeplitz Composition operator on the Hardy space $\mathcal{H}^2$ becomes complex symmetric with respect to a certain conjugation. We also study various normality conditions for the Toeplitz Composition operator on $\mathcal{H}^2$.