On faces generated by certain positive linear transformations

Abstract

This paper is divided into two parts. In the first part, suppose that K 1 and K 2 are proper cones and that A is a rank r linear transformation which maps the set of extremals of K 1 into the set of extremals of K 2. We give an upper bound for the dimension of the face generated by A in the cone Π( K 1, K 2). In the second part, we consider an indecomposable proper cone K and a nonsingular linear transformation A which maps the set of exposals of K into itself.