# Truncated Toeplitz operators and complex symmetries

## TL;DR

This paper characterizes truncated Toeplitz operators using complex symmetries, confirming a conjecture and extending previous partial results.

## Contribution

It provides a complete characterization of truncated Toeplitz operators through complex symmetries, resolving a conjecture in the field.

## Key findings

- Truncated Toeplitz operators are characterized by complex symmetries.
- The conjecture by Klis-Garlicka, Lanucha, and Ptak is proved in full generality.
- The work extends previous partial results to a comprehensive proof.

## Abstract

We show that truncated Toeplitz operators are characterized by a collection of complex symmetries. This was conjectured by Klis-Garlicka, Lanucha, and Ptak, and proved by them in some special cases.