Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0315493
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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$.

References [Enhancements On Off] (What's this?)

  • [1] A. Devinatz and M. Shinbrot, General Wiener-Hopf operators, Trans. Amer. Math. Soc. 145 (1969), 467-494. MR 40 #4800. MR 0251573 (40:4800)
  • [2] P. A. Fillmore, J. G. Stampfli and J. P. Williams, On the essential numerical range, the essential spectrum, and a problem of Halmos (to appear). MR 0322534 (48:896)
  • [3] P. R. Halmos, A Hilbert space problem book, Van Nostrand, Princeton, N.J., 1967. MR 34 #8178. MR 0208368 (34:8178)
  • [4] M. Shinbrot, On the range of general Wiener-Hopf operators, J. Math. Mech. 18 (1968/69), 587-601. MR 40 #3375. MR 0250135 (40:3375)
  • [5] J. P. Williams, Similarity and the numerical range, J. Math. Anal. Appl. 26 (1969), 307-314. MR 39 #2010. MR 0240664 (39:2010)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47A65, 47A10, 47B35

Retrieve articles in all journals with MSC: 47A65, 47A10, 47B35

Additional Information

Keywords: General Wiener-Hopf operators, numerical range
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society