PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.8, pp.2321-2326, 2004 (Journal Indexed in SCI)
Article / Article
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PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
We prove that the numerical range W (N) of an arbitrary nilpotent operator N on a complex Hilbert space H is a circle ( open or closed) with center at 0 and radius not exceeding parallel toNparallel to cos pi/n+1; where n is the power of nilpotency of N.