A Note on the Invertibility of Generalized Wiener–Hopf Operators

Abstract

We consider generalized Wiener–Hopf-operators of the form $T(A):=PA\uparrow R(P)$ in a Hilbert space, where $A$ and $P$ are linear, bounded operators, and $P$ permits a Moore–Penrose inverse. The purpose of our investigations is to derive a criterion for the invertibility of $T(A)$ in $R(P)$.