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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Anderson’s theorem for compact operators
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by Hwa-Long Gau and Pei Yuan Wu PDF
Proc. Amer. Math. Soc. 134 (2006), 3159-3162 Request permission

Abstract:

It is shown that if $A$ is a compact operator on a Hilbert space with its numerical range $W(A)$ contained in the closed unit disc $\overline {\mathbb {D}}$ and with $\overline {W(A)}$ intersecting the unit circle at infinitely many points, then $W(A)$ is equal to $\overline {\mathbb {D}}$. This is an infinite-dimensional analogue of a result of Anderson for finite matrices.
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Additional Information
  • Hwa-Long Gau
  • Affiliation: Department of Mathematics, National Central University, Chung-Li 32001, Taiwan
  • Email: hlgau@math.ncu.edu.tw
  • Pei Yuan Wu
  • Affiliation: Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan
  • Email: pywu@math.nctu.edu.tw
  • Received by editor(s): February 4, 2005
  • Received by editor(s) in revised form: March 23, 2005
  • Published electronically: June 5, 2006
  • Additional Notes: This research was partially supported by the National Science Council of the Republic of China.
  • Communicated by: Joseph A. Ball
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 3159-3162
  • MSC (2000): Primary 47A12; Secondary 47B07
  • DOI: https://doi.org/10.1090/S0002-9939-06-08699-0
  • MathSciNet review: 2231898