H-Toeplitz operators on the function spaces

Abstract

In this paper, we study several classes of H-Toeplitz operators (defined below) on the Hardy space H2. In particular, we prove that, for φ∈L∞, the adjoint of H-Toeplitz operators is hyponormal. Next, we investigate several properties of H-Toeplitz operators on the weighted Bergman spaces. Finally, we give necessary and sufficient conditions for H-Toeplitz operators to be contractive and expansive on the weighted Bergman spaces. © The Author(s), under exclusive licence to Springer-Verlag GmbH Austria, part of Springer Nature 2024.