Numerical Radius and Operator Norm Inequalities. (8th March 2009)

• Record Type: Journal Article
• Authors: Shebrawi, Khalid; Albadawi, Hussien
• Other Names: Dragomir Sever Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2009(2009)
• Publication Date: 2009-03-08
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2009/492154
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : 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 ifA andB are operators on a complex Hilbert spaceH, thenw r ( A ∗ B ) ≤ ( 1 / 2 ) ∥ | A | 2 r + | B | 2 r ∥ forr ≥ 1 . It is also shown that ifX i is normal( i = 1, 2, …, n ), then∥ ∑ i = 1 n X i ∥ r ≤ n r − 1 ∥ ∑ i = 1 n | X i | r ∥ . Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.