A Note on Nilpotent Operators

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DOI: 10.4236/apm.2012.26054    3,974 Downloads   7,536 Views  
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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.

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