Complex symmetric composition operators induced by linear fractional transformations

TL;DR

This paper fully characterizes complex symmetric composition operators with linear fractional symbols, resolving two open questions and advancing understanding in operator theory.

Contribution

It provides a complete description of such operators, addressing previously unresolved questions in the field.

Findings

Resolved two open questions on complex symmetric composition operators.

Provided a complete characterization for operators with linear fractional symbols.

Enhanced understanding of the structure of complex symmetric operators.

Abstract

In this paper we give the answers to two open questions on complex symmetric composition operators. By doing this, we give a complete description of complex symmetric composition operators whose symbols are linear fractional.