General Wiener-Hopf Operators and the Numerical Range of an Operator
Victor J. Pellegrini · Proceedings of the American Mathematical Society · 1973
Let $H$ be a separable Hilbert space and $A$ a bounded operator on $H$. For a selfadjoint projection $P$ on $H$ we consider the general Wiener-Hopf operator ${T_P}(A) = P{A_{R(P)}}$ where $R(P)$ denotes the range of $P$. In this paper we study the relation between ${T_P}(A)$ and $W(A)$, the numerical range of $A$. In particular we characterize those operators $A$ such that ${T_P}(A)$ is invertible for every $P$.