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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-5,
author = {Takeaki Yamazaki},
title = {On upper and lower bounds of the numerical radius and an equality condition},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {83-89},
zbl = {1114.47003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-5}
}
Takeaki Yamazaki. On upper and lower bounds of the numerical radius and an equality condition. Studia Mathematica, Tome 178 (2007) pp. 83-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-5/