Modulability and duality of certain cones in pluripotential theory
2010 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 361, no 2, 302-321 p.Article in journal (Refereed) Published
Let p>0, and let Ep denote the cone of negative plurisubharmonic functions with finite pluricomplex p-energy. We prove that the vector space δEp=Ep−Ep, with the vector ordering induced by the cone Ep 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 Ep in the quasi-normed space δEp is closed, generating, and has empty interior.
Place, publisher, year, edition, pages
2010. Vol. 361, no 2, 302-321 p.
Cone, δ-plurisubharmonic function, Modulability, Ordered vector space, Quasi-Banach space, Topological dual
IdentifiersURN: urn:nbn:se:umu:diva-36294DOI: 10.1016/j.jmaa.2009.07.013OAI: oai:DiVA.org:umu-36294DiVA: diva2:353468