Asymmetric truncated Toeplitz operators equal to the zero operator

TL;DR

This paper characterizes the symbols of asymmetric truncated Toeplitz operators that are identically zero, extending the understanding of these operators beyond the classical case.

Contribution

It provides a complete description of symbols leading to the zero operator in the context of asymmetric truncated Toeplitz operators.

Findings

Identifies conditions under which asymmetric truncated Toeplitz operators are zero.

Generalizes known results from classical to asymmetric cases.

Enhances understanding of the structure of these operators.

Abstract

Asymmetric truncated Toeplitz operators are compressions of multiplication operators acting between two model spaces. These operators are natural generalizations of truncated Toeplitz operators. In this paper we describe symbols of asymmetric truncated Toeplitz operators equal to the zero operator.