New York Journal of Mathematics
Volume 5 (1999) 1-16


Estelle L. Basor and Torsten Ehrhardt

On a Class of Toeplitz + Hankel Operators

Published: March 3, 1999
Keywords: Toeplitz operators, Hankel operators, Fredholm Index, Invertibility, Spectrum, Stability
Subject: 47B35; secondary: 47A10, 47A35

In this paper we study operators of the form M(φ)=T(φ)+H(φ) where T(φ) and H(φ) are the Toeplitz and Hankel operators acting on l2. We investigate the connection between Fredholmness and invertibility of M(φ) for functions φ∈ L(T). Using this relationship we establish necessary and sufficient conditions for the invertibility of M(φ) with piecewise continuous φ. Finally, we consider several stability problems related to M(φ), in particular the stability of the finite section method.


The first author was supported in part by NSF Grant DMS-9623278.

The second author was supported in part by DAAD Grant 213/402/537/5.

Author information

Estelle L. Basor:
Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407

Torsten Ehrhardt:
Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany