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Journal of Operator Theory

Volume 76, Issue 2, Fall 2016  pp. 335-349.

On the symmetrization of general Wiener-Hopf operators

Authors:  Albrecht Boettcher (1) and Frank-Olme Speck (2)
Author institution:(1) Fakultaet fuer Mathematik, Technische Universitaet Chemnitz, 09107, Germany
(2) Departamento de Matematica, Instituto Superior Tecnico, Universidade de Lisboa, 1049-001, Portugal

Summary: This article focuses on general Wiener--Hopf operators given as $W = P_2 A|_{P_1 X}$ where $X,Y$ are Banach spaces, $P_1 \in \mathcal L(X) , P_2 \in \mathcal L(Y)$ are any projectors and $A \in \mathcal L(X,Y)$ is boundedly invertible. It presents conditions for $W$ to be equivalently reducible to a Wiener--Hopf operator in a symmetric space setting where $X = Y$ and $P_1 = P_2$. The results and methods are related to the so-called Wiener--Hopf factorization through an intermediate space and the construction of generalized inverses of $W$ in terms of factorizations of $A$.

Keywords: Wiener-Hopf operator, symmetrization, factorization, generalized inverse

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