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 $N.$References
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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
- Received by editor(s): December 22, 2002
- Received by editor(s) in revised form: April 28, 2003
- Published electronically: February 12, 2004
- Communicated by: Joseph A. Ball
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2321-2326
- MSC (2000): Primary 47A12; Secondary 15A45, 42A05
- DOI: https://doi.org/10.1090/S0002-9939-04-07391-5
- MathSciNet review: 2052408