Modulability and duality of certain cones in pluripotential theory

Let p > 0, and let epsilon(P) denote the cone of negative plurisubharmonic functions with finite pluricomplex p-energy. We prove that the vector space delta epsilon(p) = epsilon(p) - epsilon(p), with the vector ordering induced by the cone epsilon(p) is sigma-Dedekind complete, and equipped with a suitable quasi-norm it is a non-separable quasi-Banach space with a decomposition property with control of the quasi-norm. Furthermore, we explicitly characterize its topological dual. The cone epsilon(p) in the quasi-normed space delta epsilon(p) is closed, generating, and has empty interior. (c) 2009 Elsevier Inc. All rights reserved.