Product of truncated Hankel and truncated Toeplitz operators

TL;DR

This paper investigates the product of truncated Hankel and Toeplitz operators on Hardy spaces, providing conditions for when the product is zero or compact, thus advancing understanding of their algebraic properties.

Contribution

It offers a new characterization of the product of truncated Hankel and Toeplitz operators, focusing on conditions for zero and compactness, which was not previously established.

Findings

Characterization of when the product is zero

Criteria for the product to be compact

Enhanced understanding of operator algebra on Hardy spaces

Abstract

A truncated Toeplitz operator is the compression of a classical Toeplitz operator on the Hardy space to a model space. A truncated Hankel operator is the compression of a Hankel operator on the Hardy space to the orthogonal complement of a model space. We study the product of a truncated Hankel operator and a truncated Toeplitz operator, and characterize when such a product is zero or compact.