# Some characterizations of asymmetric truncated Toeplitz operators

## TL;DR

This paper proves that all asymmetric truncated Toeplitz operators can be characterized using compressed shifts and specific rank-two operators, extending previous special-case results to all cases.

## Contribution

The paper generalizes existing characterizations of asymmetric truncated Toeplitz operators to encompass all cases, not just special ones.

## Key findings

- All asymmetric truncated Toeplitz operators can be characterized by compressed shifts.
- The characterization involves rank-two operators of a specific form.
- Previous results were limited to special cases, now extended universally.

## Abstract

It was recently proved that in some special cases asymmetric truncated Toeplitz operators can be characterized in terms of compressed shifts and rank-two operators of special form. In this paper we show that such characterizations hold in all cases.