Upper bounds on certain functionals defined on groups of linear operators. (English) Zbl 1149.39305
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 A. Berman and R. J. Plemmons [Math. Inequal. Appl. 1, No. 1, 149–152 (1998; Zbl 0889.15009)] 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.
MSC:
39B62 | Functional inequalities, including subadditivity, convexity, etc. |
15A18 | Eigenvalues, singular values, and eigenvectors |
15B48 | Positive matrices and their generalizations; cones of matrices |
06F20 | Ordered abelian groups, Riesz groups, ordered linear spaces |