Complex symmetry of Toeplitz operators

TL;DR

This paper introduces new conjugations to characterize complex symmetric Toeplitz operators on the Hardy space, showing equivalences with  property and discussing analytic symmetricity, thus unifying and extending previous results.

Contribution

It presents a new class of conjugations for characterizing complex symmetric Toeplitz operators and establishes their equivalence with the  property for certain classes.

Findings

Complex symmetric Toeplitz operators characterized by new conjugations

Equivalence between complex symmetricity and  property for specific classes

Extension of known results through unified treatment

Abstract

We introduce a new class of conjugations and characterize complex symmetric Toeplitz operators on the Hardy space with respect to those conjugations. Also, we prove that complex symmetricity and \uet~ property are the same for a certain class of Toeplitz operators. We also discuss the analytic symmetricity for Toeplitz operators. Our results extend several known results by providing unified ways of treating them.