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.