AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY RELATED TO NUMERICAL RADIUS OF MATRICES

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Konuralp Journal of Mathematics
Volume:5 Issue:1
AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY RELATED TO NUMERICAL RADIUS OF MATRICES

AN ARITHMETIC-GEOMETRIC MEAN INEQUALITY RELATED TO NUMERICAL RADIUS OF MATRICES

Authors : Alemeh SHEIKHHOSSEINI

Pages : 85-91

View : 46 | Download : 14

Publication Date : 2017-04-01

Article Type : Research Paper

Abstract :For positive matrices $A, B \in \mathbb{M}_{n}$ and for all $X \in \mathbb{M}_{n}$, we show that $ \omegainsert ignore into journalissuearticles values(AXA);\leq \frac{1}{2} \omegainsert ignore into journalissuearticles values(A^{2}X+XA^{2});,$ and the inequality $ \omegainsert ignore into journalissuearticles values(AXB); \leq \frac{1}{2}\omegainsert ignore into journalissuearticles values(A^{2}X+XB^{2});$ does not hold in general, where $ \omegainsert ignore into journalissuearticles values(.); $ is the numerical radius.
Keywords : Inequalities, Numerical radius, Unitarily invariant norms

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