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Modulability and duality of certain cones in pluripotential theory
Department of Natural Sciences, Engineering and Mathematics, Mid Sweden University, SE-871 88 Härnösand, Sweden.
Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland.
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
Abstract [en]

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=EpEp, 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.
Keyword [en]
Cone, δ-plurisubharmonic function, Modulability, Ordered vector space, Quasi-Banach space, Topological dual
National Category
URN: urn:nbn:se:umu:diva-36294DOI: 10.1016/j.jmaa.2009.07.013OAI: diva2:353468
Available from: 2010-09-27 Created: 2010-09-27 Last updated: 2011-10-17Bibliographically approved

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Åhag, Per
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