Toeplitz versus Hankel: semibounded operators

Abstract

Our goal is to compare various results for Toeplitz \(T\) and Hankel \(H\) operators. We consider semibounded operators and find necessary and sufficient conditions for their quadratic forms to be closable. This property allows one to define \(T\) and \(H\) as self-adjoint operators under minimal assumptions on their matrix elements. We also describe domains of the closed Toeplitz and Hankel quadratic forms.

Keywords

• semibounded Toeplitz
• Hankel and Wiener-Hopf operators
• closable and closed quadratic forms