# 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 $A$.

**DOI: **http://dx.doi.org/10.7900/jot.2015nov21.2112

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

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