Geodesic
An Operator Karamata Inequality
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4

Voir la notice de l'article provenant de la source Bulletin of the Malaysian Mathematical Sciences Society website

We present an operator version of the Karamata inequality. More precisely, we prove that if $A$ is a selfadjoint element of a unital $C^*$-algebra $\mathscr{A}$ ,ρ is a state on $\mathscr{A}$ , the functions f ;g are continuous on the spectrum σ(A) of A such that $0$ $m$ $1$ ≤$f(s)$ ≤ $M$ $1$ , $0$ $m$ $2$ ≤ $g(s)$ ≤ $M$ $2$ for all $s\in \sigma(A)$ and $K=\left(\sqrt{m_1m_2}+\sqrt{M_1M_2}\right)/\left(\sqrt{m_1M_2}+\sqrt{M_1m_2}\right)$ then

$K^{-2}\le \frac{\rho(f(A)g(A))}{\rho(f(A)) \rho(g(A))}\le K^2.$

We also give some applications.
Classification : Primary 47A63; Secondary 47B25, 15A60 
M. S. Moslehian; M. Niezgoda; R. Rajić. An Operator Karamata Inequality. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 4. http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a2/
@article{BMMS_2014_37_4_a2,
     author = {M. S. Moslehian and M. Niezgoda and R. Raji\'c},
     title = {An {Operator} {Karamata} {Inequality}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2014},
     volume = {37},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_4_a2/}
}
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