Upper bounds on certain functionals defined on groups of linear operators

Abstract

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.