Positive linear maps on normal matrices

TL;DR

This paper investigates bounds on positive linear maps applied to normal matrices, deriving sharp inequalities especially for the Schur product, enhancing understanding of matrix transformations in operator theory.

Contribution

It introduces new bounds on positive linear maps of normal matrices, including sharp inequalities for the Schur product, advancing matrix analysis techniques.

Findings

|F(N)| is bounded by linear combinations in the unitary orbit of F(|N|)

Derived sharp inequalities for positive linear maps on normal matrices

Enhanced understanding of matrix transformations in operator theory

Abstract

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.