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.