On estimate for numerical radius of some contractions

• Date: 2006
• Main Authors: Karaev, M. T., Караєв, М. Т.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3536
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

For the numerical radius of an arbitrary nilpotent operator T on a Hilbert space H, Haagerup and de la Harpe proved the inequality \(w(T) \leqslant \left\| T \right\|cos\frac{\pi }{{n + 1}}\), where $n \geq 2$ is the nilpotency order of the operator T. In the present paper, we prove a Haagerup-de la...