The numerical range of a nilpotent operator on a Hilbert space-Reference-Cited by-同舟云学术

The numerical range of a nilpotent operator on a Hilbert space

Published:2004-02-12 Issue:8 Volume:132 Page:2321-2326
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Karaev Mubariz

Abstract

We prove that the numerical range W ( N ) W\left ( N\right ) of an arbitrary nilpotent operator N N on a complex Hilbert space H H is a circle (open or closed) with center at 0 0 and radius not exceeding ‖ N ‖ cos ⁡ π n + 1 , \left \| N\right \| \cos \frac {\pi }{n+1}, where n n is the power of nilpotency of N . N.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2004-132-08/S0002-9939-04-07391-5/S0002-9939-04-07391-5.pdf

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