Journal article

Modulability and duality of certain cones in pluripotential theory

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Author list: Åhag, Per

Publication year: 2010

Start page: 302

End page: 321

Number of pages: 20

ISSN: 0022-247X

DOI: http://dx.doi.org/10.1016/j.jmaa.2009.07.013

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Abstract

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 s-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.


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