Essentially commuting dual truncated Toeplitz operators

TL;DR

This paper characterizes when two dual truncated Toeplitz operators essentially commute and when their semicommutator is compact, using tools like Hankel and Toeplitz operators and function algebras.

Contribution

It provides a complete characterization of essential commutativity and compactness conditions for dual truncated Toeplitz operators, advancing understanding of their algebraic properties.

Findings

Criteria for essential commutativity of dual truncated Toeplitz operators

Conditions under which the semicommutator is compact

Use of Hankel and Toeplitz operators in the analysis

Abstract

In this paper, we completely characterize when two dual truncated Toeplitz operators are essentially commuting and when the semicommutator of two dual truncated Toeplitz operators is compact. Our main idea is to study dual truncated Toeplitz operators via Hankel operators, Toeplitz operators and function algebras.