On estimate for numerical radius of some contractions - Karaev, M. T. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
For the numerical radius of an arbitrary nilpotent operator T on a Hilbert space H, Haagerup and de la Harpe proved the inequality \(w(T) \| T \|cosπ n + 1 \), 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.