Bishop-Phelps cones given by an equation in Banach spaces

In this work, we study Bishop-Phelps cones (briefly, BP cones) given by an equation in Banach spaces. Due to the special form, these cones enjoy interesting properties. We show that nontrivial BP cones given by an equation form a “large family” in some sense in any Banach space and they can be used to characterize … Read more

On the irreducibility, Lyapunov rank, and automorphisms of speical Bishop-Phelps cones

Motivated by optimization considerations, we consider special Bishop-Phelps cones in R^n which are of the form {(t,x): t \geq ||x||} for some norm on R^(n-1). We show that for n bigger than 2, such cones are always irreducible. De fining the Lyapunov rank of a proper cone K as the dimension of the Lie algebra of … Read more

A Generalization of a Theorem of Arrow, Barankin and Blackwell to a Nonconvex Case

The paper presents a generalization of a known density theorem of Arrow, Barankin, and Blackwell for properly efficient points defined as support points of sets with respect to monotonically increasing sublinear functions. This result is shown to hold for nonconvex sets of a reflexive Banach space partially ordered by a Bishop–Phelps cone. Citation Department of … Read more