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.References
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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