The numerical range of a nilpotent operator on a Hilbert space

Karaev, Mubariz

doi:10.1090/S0002-9939-04-07391-5

The numerical range of a nilpotent operator on a Hilbert space
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by Mubariz T. Karaev PDF

Proc. Amer. Math. Soc. 132 (2004), 2321-2326 Request permission

Abstract:

We prove that the numerical range $W\left ( N\right )$ 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 $\left \| N\right \| \cos \frac {\pi }{n+1},$ where $n$ is the power of nilpotency of $N.$

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