535. Conditional Lpspaces and the duality of modules over falgebras
by S. CerreiaVioglio, M. Kupper, F. Maccheroni, M. Marinacci, N. Vogelpoth
Motivated by dynamic asset pricing, we extend the dual pairstheory of Dieudonné(1942) and Mackey (1945) to pairs of modules over a Dedekind complete falgebra with multiplicative unit. The main tools are:
 a HahnBanach Theorem for modules of this kind;
 a topology on the falgebra 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 is considered.
As a leading example, we study in some detail the duality of conditional Lpspaces.
Keywords: Dual pairs, HahnBanach Theorem for modules, complete L0normed modules, automatic continuity
