On upper and lower bounds of the numerical radius and an equality condition
Takeaki Yamazaki · Studia Mathematica · 2007
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 conditio