Journal of Operator Theory

Volume 51, Issue 2, Spring 2004 pp. 411-433.

Factorization theory for a class of Toeplitz + Hankel operators

Authors: Estelle L. Basor (1) and Torsten Ehrhardt (2)
Author institution: (1) Department of Mathematics, California Polytechnic State University, San Luis Obispo, CA 93407, USA
(2) Fakultaet fuer Mathematik, Technische Universitaet Chemnitz, 09107 Chemnitz, Germany

Summary: In this paper we study operators of the form $M(\phi)=T(\phi)+H(\phi)$ where $T(\phi)$ and $H(\phi)$ are the Toeplitz and Hankel operators acting on $H^p(\T)$ with generating function $\phi\in L^\iy(\T)$. It turns out that $M(\phi)$ is invertible if and only if the function $\phi$ admits a certain kind of generalized factorization.

Keywords: Toeplitz operator, Hankel operator, Fredholm theory, factorization

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