Weak topologies for modules over rings of bounded random variables

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:421

Article

Eisele, Karl-Theodor^1,2  Taieb, Sonia³ 

[1] Univ Strasbourg, Lab Rech Gest & Econ, PEGE, F-67085 Strasbourg, France

[2] Univ Strasbourg, Inst Rech Math Avancee, PEGE, F-67085 Strasbourg, France

[3] Univ El Manar, Fac Sci, El Manar 2092, Tunisia

关键词: Locally convex module over L degrees;    Extended Hahn Banach and separation theorems;    Bipolar theorem;    General Krein Smulian and;    Alaoglu-Bourbaki theorem for modules;   

DOI  :  10.1016/j.jmaa.2014.07.062

来源: Elsevier

【 摘 要 】

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 lambda = L-infinity (G). Their topology is determined by lambda-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 lambda-module is introduced, one can establish a module version of the Bipolar theorem. We also prove the Krein Smulian as well as the Alaoglu Bourbaki theorem for lambda-modules. For Banach A-modules their reflexivity is characterized by a compactness criterium in a (very) weak-* topology. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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