The numerical range of a nilpotent operator on a Hilbert space

Karaev M.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.132, sa.8, ss.2321-2326, 2004 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 132 Konu: 8
  • Basım Tarihi: 2004
  • Doi Numarası: 10.1090/s0002-9939-04-07391-5
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.2321-2326

Özet

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.