U. Haagerup and P. de la Harpe, “The Numerical Radius of a Nilpotent Operator on a Hilbert Space,” Proceedings of the American Mathematical Society, Vol. 115, 1999, pp. 371-379.

has been cited by the following article:

• TITLE: A Note on Nilpotent Operators

  AUTHORS: Abhay K. Gaur

  KEYWORDS: Numerical Range; Numerical Radius; Nilpotent Operator Weighted Shift; Eigenvalues

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.6, November 9, 2012

  ABSTRACT: We find that a bounded linear operator T on a complex Hilbert space H satisfies the norm relation |||T|na|| =2q, for any vector a in H such that q≤（||Ta||-4-1||Ta||2)≤1.A partial converse to Theorem 1 by Haagerup and Harpe in [1] is suggested. We establish an upper bound for the numerical radius of nilpotent operators.