Complex symmetry of linear fractional composition operators on a half-plane

TL;DR

This paper characterizes when linear fractional composition operators on the Hardy space of the right half-plane are cohyponormal or complex symmetric, providing a detailed understanding of their symmetry properties.

Contribution

It offers a complete characterization of cohyponormality and complex symmetry for linear fractional composition operators on the right half-plane Hardy space.

Findings

Identifies conditions for cohyponormality of these operators.

Finds conjugations that make the operators complex symmetric.

Provides a classification of symmetry properties for these operators.

Abstract

We investigate the bounded composition operators induced by linear fractional self-maps of the right half-plane $\mathbb{C}_+$ on the Hardy space $H^2(\mathbb{C}_+).$ We completely characterize which of these operators are cohyponormal and we find conjugations for the linear fractional composition operators that are complex symmetric.