ELA, Volume 15, pp. 191-200, June 2006, abstract.
Upper Bounds on Certain Functionals Defined on
Groups of Linear Operators
Marek Niezgoda
The problem of estimating certain functionals defined
on a group of linear operators generating a group induced
cone (GIC) ordering is studied. A result of Berman and
Plemmons [Math. Inequal. Appl., 2(1):149--152, 1998] is
extended from the sum function to Schur-convex functions.
It is shown that the problem has a closed connection with
both Schur type inequality and weak group majorization.
Some applications are given for matrices.