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The numerical range of a nilpotent operator on a Hilbert space

Author(s): Mubariz T. Karaev
Journal: Proc. Amer. Math. Soc. 132 (2004), 2321-2326.
MSC (2000): Primary 47A12; Secondary 15A45, 42A05
Posted: February 12, 2004
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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 $\left\Vert N\right\Vert \cos \frac{\pi }{n+1},$ where $n$ is the power of nilpotency of $N.$

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Additional Information:

Mubariz T. Karaev
Affiliation: Institute For Mathematics And Mechanics, Azerbaijanian National Academy of Sciences, F.Agaev, 9, 370141 Baku, Azerbaijan
Address at time of publication: Department of Mathematics, Faculty of Arts and Sciences, Suleyman Demirel University, 32260 Isparta, Turkey
Email: garayev@fef.sdu.edu.tr

DOI: 10.1090/S0002-9939-04-07391-5
PII: S 0002-9939(04)07391-5
Keywords: Numerical range, numerical radius, nilpotent operator, model operator
Received by editor(s): December 22, 2002
Received by editor(s) in revised form: April 28, 2003
Posted: February 12, 2004
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society

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