Positive linear functionals and the order cone
Let P be the cone of \(n\times n\) complex matrices with positive semi- definite Hermitean part and let \(P^*\) be the dual cone. The paper shows equality of two expressions defined for \(p\in \partial P\) and q arbitrary, namely max Re(cq) over all \(c\in P^*\) satisfying \(cI=1\) and \(Re(cp)=0\) equals max Re(\(\xi\),q\(\xi)\) over all vectors \(\xi\) of norm one satisfying \((p+p^*)\xi =0\).
scientific article; zbMATH DE number 4112782