A Monge-Ampère norm for delta-plurisubharmonic functions

Abstract

We consider differences of plurisubharmonic functions in the energy class $\mathcal{F}$ as a linear space, and equip this space with a norm, depending on the generalized complex Monge-Ampère operator, turning the linear space into a Banach space $\delta \mathcal{F}$. Fundamental topological questions for this space is studied, and we prove that $\delta\mathcal{F}$ is not separable. Moreover we investigate the dual space. The study is concluded with comparison between $\delta \mathcal{F}$ and the space of delta-plurisubharmonic functions, with norm depending on the total variation of the Laplace mass, studied by the first author in an earlier paper [7].