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