Commuting Nilpotent Operators and Maximal Rank


ÖZTÜRK S.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.4, no.4, pp.901-904, 2010 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.1007/s11785-009-0029-x
  • Title of Journal : COMPLEX ANALYSIS AND OPERATOR THEORY
  • Page Numbers: pp.901-904

Abstract

Let X, (X) over tilde be commuting nilpotent matrices over k with nilpotency p(t), where k is an algebraically closed field of positive characteristic p. We show that if X - (X) over tilde is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if (X) over tilde is of maximal rank.