The numerical range of a nilpotent operator on a Hilbert space

Karaev M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.132, no.8, pp.2321-2326, 2004 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 132 Issue: 8
  • Publication Date: 2004
  • Doi Number: 10.1090/s0002-9939-04-07391-5
  • Title of Journal : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.2321-2326

Abstract

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.