Factorization theory for a class of Toeplitz + Hankel operators

arXiv:math/0204038

Abstract

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