On the duality operator of a convex cone
Convex cones in the euclidean space \(R^ n\) are considered, and properties of the duality operator \(d_ K\) are studied not only for so called proper cones K, but also for general ones. Several propositions are proved concerning face lattices of convex sets and cones. The main results say in which cases, for K closed, the operator \(d_ K\) is injective (surjective). Some sufficient conditions are given for a cone to be the point's cone (at the origin) of a compact convex set.
scientific article; zbMATH DE number 3881396