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Anderson's theorem for compact operators
Authors:
Hwa-Long Gau and Pei Yuan Wu
Journal:
Proc. Amer. Math. Soc. 134 (2006), 3159-3162
MSC (2000):
Primary 47A12; Secondary 47B07
Posted:
June 5, 2006
MathSciNet review:
2231898
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Abstract: It is shown that if  is a compact operator on a Hilbert space with its numerical range  contained in the closed unit disc  and with  intersecting the unit circle at infinitely many points, then  is equal to  . 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
DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08699-0
PII:
S 0002-9939(06)08699-0
Keywords:
Numerical range,
compact operator
Received by editor(s):
February 4, 2005
Received by editor(s) in revised form:
March 23, 2005
Posted:
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
Article copyright:
© Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain after
28 years from publication.
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