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Proceedings of the American Mathematical Society

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

 

 

General Wiener-Hopf operators and the numerical range of an operator


Author: Victor J. Pellegrini
Journal: Proc. Amer. Math. Soc. 38 (1973), 141-146
MSC: Primary 47A65; Secondary 47A10, 47B35
DOI: https://doi.org/10.1090/S0002-9939-1973-0315493-1
MathSciNet review: 0315493
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Abstract: 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$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0315493-1
Keywords: General Wiener-Hopf operators, numerical range
Article copyright: © Copyright 1973 American Mathematical Society