Copyright © 2009 Khalid Shebrawi and Hussien Albadawi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
A general inequality involving powers of the numerical radius for sums
and products of Hilbert space operators is given. This inequality generalizes several recent
inequalities for the numerical radius, and includes that if and are operators on a complex
Hilbert space , then for . It is also shown that if is normal , then . Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.