Product of truncated Hankel and truncated Toeplitz operators

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.