Asymptotically Orthonormal Basis and Toeplitz operators

Abstract

Recently, M. Mitkovski gave a criterion for the basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated Toeplitz operator, in the spirit of the celebrated work of Khrushchev-Nikolski-Pavlov. In our paper, we extend the results of Mitkovski to model spaces associated with meromorphic inner functions and we also give an analogue for the property of being an asymptotically orthonormal basis.