On the reduction of general Wiener–Hopf operators

Abstract

The aim of this work is to present criteria for the equivalent reduction of general Wiener–Hopf operators $W \,=\,P_{2}A|{P_{1} X}\, \text{where}\, X, Y$ 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 a bounded linear operator, namely, to more special forms where X = Y and possibly P₁ = P₂ and/or A is invertible or even where A is a cross factor.

This is carried out with the help of operator relations: equivalence, equivalence after extension, matricial coupling and further related relations. Examples are given for the occurrence of different operator relations in applications.

Dedicated to Rien Kaashoek on the occasion of his 80th birthday