Modulability and duality of certain cones in pluripotential theory

Let p > 0 , and let E p denote the cone of negative plurisubharmonic functions with finite pluricomplex p-energy. We prove that the vector space δ E p = E p − E p , with the vector ordering induced by the cone E p is σ-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 E p in the quasi-normed space δ E p is closed, generating, and has empty interior.