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

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2016

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Cerreia-Vioglio, Simone
Maccheroni, Fabio
Marinacci, Massimo
Vogelpoth, Nicolas

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https://doi.org/10.1016/j.jmaa.2016.06.018
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Journal of Mathematical Analysis and Applications. 2016, 444(2), pp. 1045-1070. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2016.06.018

Zusammenfassung

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.

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ISO 690CERREIA-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. 2016, 444(2), pp. 1045-1070. ISSN 0022-247X. eISSN 1096-0813. Available under: doi: 10.1016/j.jmaa.2016.06.018
BibTex
@article{CerreiaVioglio2016Condi-37298,
  year={2016},
  doi={10.1016/j.jmaa.2016.06.018},
  title={Conditional Lp-spaces and the duality of modules over f-algebras},
  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}
}
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