Fredholm criteria in a C*-algebra acting on the Hardy space of the bi-disc with applications to composition operators

Abstract

In this work we give a Fredholm criteria for the operators in the C*-algebra generated by certain Toeplitz operators and Fourier multipliers acting on the Hardy space of the bidisc. With help of the obtained results we also completely characterize the essential spectra of quasi-parabolic composition operators on the Hardy spaces of the bi-disc. (C) 2019 Elsevier Inc. All rights reserved.