Conditional Lp-spaces and the duality of modules over f-algebras

Type of Publication: Journal article
Publication status: Published
Author: Cerreia-Vioglio, Simone; Kupper, Michael; Maccheroni, Fabio; Marinacci, Massimo; Vogelpoth, Nicolas
Year of publication: 2016
Published in: Journal of Mathematical Analysis and Applications ; 444 (2016), 2. - pp. 1045-1070. - ISSN 0022-247X. - eISSN 1096-0813
DOI (citable link): https://dx.doi.org/10.1016/j.jmaa.2016.06.018
Summary:
Motivated by dynamic asset pricing, we extend the dual pairs' theory of Dieudonné (1942) and Mackey (1945) to pairs of modules over a Dedekind complete f-algebra with multiplicative unit. The main tools are:

• a Hahn–Banach Theorem for modules of this kind;

• a topology on the f -algebra that has the special feature of coinciding with the norm topology when the algebra is a Banach algebra and with the strong order topology of Filipovic, Kupper, and Vogelpoth (2009), when the algebra of all random variables on a probability space (Ω,G,P)(Ω,G,P) is considered.

As a leading example, we study in some detail the duality of conditional LpLp-spaces.
Subject (DDC): 530 Physics
Bibliography of Konstanz: Yes

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CERREIA-VIOGLIO, Simone, Michael KUPPER, Fabio MACCHERONI, Massimo MARINACCI, Nicolas VOGELPOTH, 2016. Conditional Lp-spaces and the duality of modules over f-algebras. In: Journal of Mathematical Analysis and Applications. 444(2), pp. 1045-1070. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2016.06.018

@article{CerreiaVioglio2016Condi-37298, title={Conditional Lp-spaces and the duality of modules over f-algebras}, year={2016}, doi={10.1016/j.jmaa.2016.06.018}, number={2}, volume={444}, issn={0022-247X}, journal={Journal of Mathematical Analysis and Applications}, pages={1045--1070}, author={Cerreia-Vioglio, Simone and Kupper, Michael and Maccheroni, Fabio and Marinacci, Massimo and Vogelpoth, Nicolas} }

2017-02-10T08:40:12Z 2017-02-10T08:40:12Z Motivated by dynamic asset pricing, we extend the dual pairs' theory of Dieudonné (1942) and Mackey (1945) to pairs of modules over a Dedekind complete f-algebra with multiplicative unit. The main tools are:<br /><br />• a Hahn–Banach Theorem for modules of this kind;<br /><br />• a topology on the f -algebra that has the special feature of coinciding with the norm topology when the algebra is a Banach algebra and with the strong order topology of Filipovic, Kupper, and Vogelpoth (2009), when the algebra of all random variables on a probability space (Ω,G,P)(Ω,G,P) is considered.<br /><br />As a leading example, we study in some detail the duality of conditional LpLp-spaces. Kupper, Michael Marinacci, Massimo Vogelpoth, Nicolas Kupper, Michael 2016 eng Marinacci, Massimo Cerreia-Vioglio, Simone Cerreia-Vioglio, Simone Conditional Lp-spaces and the duality of modules over f-algebras Maccheroni, Fabio Maccheroni, Fabio Vogelpoth, Nicolas

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