PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.132, sa.8, ss.2321-2326, 2004 (SCI İndekslerine Giren Dergi)
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.