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Anderson's theorem for compact operators |
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| Authors: | Hwa-Long Gau Pei Yuan Wu |
| Institution: | Department of Mathematics, National Central University, Chung-Li 32001, Taiwan ; Department of Applied Mathematics, National Chiao Tung University, Hsinchu 300, Taiwan |
| 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. |
| Keywords: | Numerical range compact operator |
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