Inequalities involving extreme eigenvalues and positive linear maps

Abstract

In this paper, we discuss some inequalities involving unital positive linear maps and extreme eigenvalues of positive semidefinite (or positive definite) matrices. We also obtain a lower bound for condition number; and a lower bound for Kantorovich ratio. In addition, some inequalities involving traces and extreme eigenvalues of a given $n\times n$ complex matrix are obtained when all of its eigenvalues are nonnegative.