Some generalisations of the inequalities for positive linear maps

TL;DR

This paper generalizes existing inequalities for positive unital linear maps on matrix algebras, leading to new and old inequalities involving eigenvalues of Hermitian matrices and providing several positive semidefinite matrices.

Contribution

It introduces generalized inequalities for positive unital linear maps, expanding the theoretical framework and deriving new eigenvalue inequalities for Hermitian matrices.

Findings

Derived new inequalities involving eigenvalues of Hermitian matrices

Provided several examples of positive semidefinite matrices

Extended classical inequalities to broader classes of linear maps

Abstract

We obtain generalisations of some inequalities for positive unital linear maps on matrix algebra. This also provides several positive semidefinite matrices and we get some old and new inequalities involving the eigenvalues of a Hermitian matrix.