Perturbations of Toeplitz operators on vector-valued Hardy spaces

Abstract

In this article, we completely classify invariant subspaces of finite-rank perturbations of a class of Toeplitz operators on vector-valued Hardy spaces. As a consequence, in the vector-valued setting, we characterize invariant and almost invariant subspaces of a class of Toeplitz operators, as well as nearly invariant subspaces associated with certain Blaschke-based operators. We further treat the finite defect case for these nearly invariant subspaces.