Asymmetric truncated Toeplitz operators and conjugations

TL;DR

This paper explores the properties of asymmetric truncated Toeplitz operators and their conjugations, revealing unique symmetries and connections to Hankel operators within the framework of model spaces.

Contribution

It introduces new conjugation properties and establishes links between asymmetric truncated Toeplitz operators and Hankel operators, advancing understanding of their symmetries.

Findings

Unique conjugation properties in model spaces

Relations between asymmetric truncated Toeplitz and Hankel operators

Characterization of C-symmetry in these operators

Abstract

Truncated Toeplitz operators in a model space are C--symmetric with respect to a natural conjugation in that space. We show that this and another conjugation associated to an orthogonal decomposition possess unique properties and we study their relations with asymmetric truncated Toeplitz operators in terms of C--symmetry. New connections with Hankel operators are established through this approach.