Axiomatization of the index of pointedness for closed convex cones
Alberto Seeger | Iusem, Alfredo
poited cone | solid cone | index of pointedness | duality
Let C(H) denote the class of closed convex cones in a Hilbert space H.One possible way of measuring the degree of pointedness of a cone K is to evaluate the distance from K to the set of all nonpointed cones. This approach has been explored in detail in a previous work of ours. We go now beyond this particular choice and set up an axiomatic background for addressing this issue. We define an index of pointedness as a function f from C(H) to R satisfying certain axioms. The number f(K) is intended, of course, to measure the degree of pointedness of K. Although several important examples are discussed in order to illustrate the theory in action,the emphasis in this work lies in the general properties that can be derived directly from the axiomatic model.