In this paper we derive some improvements of means inequalities for Hilbert space operators. More precisely, we obtain refinements and reverses of the arithmetic-geometric operator mean inequality. As an application, we also deduce an improved variant for the refined arithmetic--Heinz mean inequality. We also present some eigenvalue inequalities for differences of certain operator means.
"Refinements and reverses of means inequalities for Hilbert space operators." Banach J. Math. Anal. 7 (2) 15 - 29, 2013. https://doi.org/10.15352/bjma/1363784220