Characterizations of asymmetric truncated Toeplitz operators

TL;DR

This paper investigates asymmetric truncated Toeplitz operators with $L^2$ symbols between different model spaces, providing characterizations and symbol conditions for zero operators, advancing understanding of their structure.

Contribution

It offers new characterizations of asymmetric truncated Toeplitz operators and describes symbols that yield zero operators, extending prior theoretical frameworks.

Findings

Characterizations in terms of rank two operators

Description of symbols for zero operators

Insights into the structure of asymmetric truncated Toeplitz operators

Abstract

The aim of this paper is to investigate asymmetric truncated Toeplitz operators with $L^2$ symbols between two different model spaces given by inner functions such that one divides the other. Characterizations of these operators are given in terms of rank two operators. A description of the class of symbols for which the corresponding asymmetric truncated Toeplitz operator is equal to the zero operator is also given.