On estimate for numerical radius of some contractions

For the numerical radius of an arbitrary nilpotent operator T on a Hilbert space H, Haagerup and de la Harpe proved the inequality , where n ≥ 2 is the nilpotency order of the operator T. In the present paper, we prove a Haagerup-de la Harpe-type inequality for the numerical radius of contractions from more general classes. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 10, pp. 1335–1339, October, 2006.