We consider differences of plurisubharmonic functions in the energy classF 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 δF. Fundamental topological questions for this space is studied, and we prove that δF is not separable. Moreover we investigate the dual space. The study is concluded with comparison between δF 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