A Note on Nilpotent Operators ()
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.
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A. Gaur, "A Note on Nilpotent Operators," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 367-370. doi: 10.4236/apm.2012.26054.
Conflicts of Interest
The authors declare no conflicts of interest.
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