Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615654 | Journal of Mathematical Analysis and Applications | 2015 | 24 Pages |
Abstract
In order to establish a functional analytic basis for representation theorems for conditional and multi-period risk measures, we study locally convex modules over the ring λ=Lâ(G). Their topology is determined by λ-seminorms. As expected, central mathematical tools of the analysis are Hahn-Banach type and separation theorems which however have to be treated more carefully in the module case. Once a dual λ-module is introduced, one can establish a module version of the Bipolar theorem. We also prove the Krein-Å mulian as well as the Alaoglu-Bourbaki theorem for λ-modules. For Banach λ-modules their reflexivity is characterized by a compactness criterium in a (very) weak-* topology.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Karl-Theodor Eisele, Sonia Taieb,