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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.