On the structure of the cone of positive operators

[[abstract]]If K1 is a proper cone in Rn1 and K2 is a proper cone in Rn2, then, as is well known, the set π(K1, K2), which consists of all n2 x n1 real matrices which take K1 into K2, forms a proper cone in the space Rn2, n1. In this paper a study of this cone is made, with particular emphasis on its faces and duality operator. A face of π(K1, K2) is called simple if it is composed of all matrices in π(K1, K2) which take some fixed face of K1 into some fixed face of K2. Maximal faces of π(K1, K2) are characterized as a particular kind of simple faces. Relations between the duality operator of π(K1, K2) and those of K1 and K2 are obtained. Among many other results, it is proved that dπ(K1, K2), the duality operator of π(K1, K2), is injective if and only if dK2 is injective and each face of π(K1, K2) is an intersection of simple faces. Two open questions are posed.[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]US