It is shown that if A is a bounded linear operator on a complex Hilbert space, then 1/4 ||A*A + AA*|| ≤ (w(A))² ≤ 1/2 ||A*A + AA*||, where w(·) and ||·|| are the numerical radius and the usual operator norm, respectively. These inequalities lead to a considerable improvement of the well known inequalities 1/2 ||A|| ≤ w(A) ≤ || A||. Numerical radius inequalities for products and commutators of operators are also obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-5,
author = {Fuad Kittaneh},
title = {Numerical radius inequalities for Hilbert space operators},
journal = {Studia Mathematica},
volume = {166},
year = {2005},
pages = {73-80},
zbl = {1072.47004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-5}
}
Fuad Kittaneh. Numerical radius inequalities for Hilbert space operators. Studia Mathematica, Tome 166 (2005) pp. 73-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm168-1-5/