On the structure of the cone of positive operators (Q1187509)

Let \(K_ 1,K_ 2\) be proper cones in \(\mathbb{R}^{n_ 1}\) and \(\mathbb{R}^{n_ 2}\), respectively, and let \(\pi(K_ 1,K_ 2)=\{A\in\mathbb{R}^{n_ 1,n_ 2}:AK_ 1\subset K_ 2\}\). The author investigates the cone \(\pi(K_ 1,K_ 2)\), with particular emphasis on its faces and duality operator. Two open problems are posed at the end.