Numerical Radius and Operator Norm Inequalities | Zendy

Khalid Shebrawi | Zendy; Hussien Albadawi | Zendy

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Numerical Radius and Operator Norm Inequalities

Author(s) -

Khalid Shebrawi,

Hussien Albadawi

Publication year - 2009

Publication title -

journal of inequalities and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.735

H-Index - 50

eISSN - 1029-242X

pISSN - 1025-5834

DOI - 10.1155/2009/492154

Subject(s) - mathematics , norm (philosophy) , inequality , operator (biology) , operator norm , pure mathematics , algebra over a field , mathematical analysis , operator theory , biochemistry , chemistry , repressor , political science , transcription factor , law , gene

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 A and B are operators on a complex Hilbert space H, then wr(A∗B)≤(1/2)‖|A|2r+|B|2r‖ for r≥1. It is also shown that if Xi is normal (i=1,2,…,n), then ‖∑i=1nXi‖r≤nr−1‖∑i=1n|Xi|r‖. Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented

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