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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the invertibility of general Wiener-Hopf operators


Author: John Reeder
Journal: Proc. Amer. Math. Soc. 27 (1971), 72-76
MSC: Primary 47.10
MathSciNet review: 0267405
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Abstract: Let $ \mathfrak{H}$ be a separable Hilbert space, $ \mathfrak{B}$ the set of bounded linear operators on $ \mathfrak{H}$, and $ P$ an orthogonal projection on $ \mathfrak{H}$. Denote the range of $ P$ by $ R(P)$. Let $ A$ belong to $ \mathfrak{B}$. The general Wiener-Hopf operator associated with $ A$ and $ P$ is defined by $ {T_P}(A) = PA\vert R(P)$, the vertical bar denoting restriction. Let $ Q = I - P$. The purpose of this paper is to disprove the general conjecture that if $ A$ is an invertible element of $ \mathfrak{B}$, then the invertibility of $ {T_P}(A)$ implies the invertibility of $ {T_Q}(A)$. We also disprove the conjecture in an interesting special case.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0267405-5
Keywords: General Wiener-Hopf operators
Article copyright: © Copyright 1971 American Mathematical Society