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arXiv · 1608.08709

Vector duality via conditional extension of dual pairs

Samuel Drapeau·Asgar Jamneshan·Michael Kupper
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Abstract

A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions $f\colon X\to \overline{L^0}$ is established where $(X,Y,\langle \cdot,\cdot \rangle)$ is a dual pair of Banach spaces and $\overline{L^0}$ is the set of all extended real-valued measurable functions. We provide a concept of lower semi-continuity which is shown to be equivalent to the existence of a dual representation in terms of elements in the Bochner space $L^0(Y)$. To derive the duality result, several conditional completions and extensions are constructed. This is an earlier version of arXiv e-print 1708.03127, where the main results were formulated in an abstract setting of conditional completions, conditional extensions and conditional real numbers.

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Samuel Drapeau, Asgar Jamneshan, Michael Kupper. 2016-08-31. Vector duality via conditional extension of dual pairs. https://arxiv.org/abs/1608.08709

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