On the invertibility of general Wiener-Hopf operators
Abstract: Let be a separable Hilbert space, the set of bounded linear operators on , and an orthogonal projection on . Denote the range of by . Let belong to . The general Wiener-Hopf operator associated with and is defined by , the vertical bar denoting restriction. Let . The purpose of this paper is to disprove the general conjecture that if is an invertible element of , then the invertibility of implies the invertibility of . We also disprove the conjecture in an interesting special case.
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