- Konuralp Journal of Mathematics
- Vol: 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 : 8 | Download : 3
Publication Date : 2017-04-01
Article Type : Research
Abstract :For positive matrices $A, B \in \mathbb{M}_{n}$ and for all $X \in \mathbb{M}_{n}$, we show that $ \omega(AXA)\leq \frac{1}{2} \omega(A^{2}X+XA^{2}),$ and the inequality $ \omega(AXB) \leq \frac{1}{2}\omega(A^{2}X+XB^{2})$ does not hold in general, where $ \omega(.) $ is the numerical radius.Keywords : Inequalities, Numerical radius, Unitarily invariant norms.