On upper and lower bounds of the numerical radius and an equality condition
Tom 178 / 2007
Studia Mathematica 178 (2007), 83-89 MSC: Primary 47A12; Secondary 47A30, 47A20. DOI: 10.4064/sm178-1-5
We give an inequality relating the operator norm of $T$ and the numerical radii of $T$ and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.