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

Yıl 2017, Cilt: 5 Sayı: 1, 85 - 91, 01.04.2017

Alemeh Sheıkhhosseını

Öz

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.

Anahtar Kelimeler

Inequalities, Numerical radius, Unitarily invariant norms.

Kaynakça

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