Inequalities involving eigenvalues and positive linear functionals (Q6649412)

The authors study inequalities for the eigenvalues of Hermitian matrices using unital positive linear functionals. The primary focus is on deriving bounds for the arithmetic mean of the extreme eigenvalues of Hermitian matrices and generalizing existing inequalities in matrix theory. The authors also establish bounds for specific functionals and extend the inequalities to encompass the roots and spans of polynomials. Numerical examples are provided to illustrate the results. The methods employed are based on established techniques in matrix theory.