Using an identity for effective resistances, we find a relationship between the arithmetic-geometric index and the global ciclicity index. Also, with the help of majorization, we find tight upper and lower bounds for the arithmetic-geometric index.

In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that any positive map Λ : Md(C) → Md(C) can be written as the difference between two completely positive maps Λ = Λ1 − Λ2, we propose a possible way to generalize...

We introduce a transport-majorization argument that establishes majorization in the convex order between two densities, based on control of gradient transportation map them. As applications, we give elementary derivations some delicate Fourier analytic inequalities, which turn yield geometric “slicing-inequalities” both continuous and discrete settings. further consequence our investigation pro...