Vector duality via conditional extension of dual pairs

2016/08/31 by Samuel Drapeau, Drapeau, Samuel, Asgar Jamneshan +3 · 1 citation
Computer Science · Decision Sciences · Mathematics · #03C90 #46A20 #46B22 #54C20 #54D35 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Variational Analysis #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.1608.08709

openalex publication_date 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Fenchel-Moreau type duality for proper convex and lower semi-continuous functions f\colon X→ L⁰ is established where (X,Y,⟨ ⋅,⋅ ⟩) is a dual pair of Banach spaces and L⁰ 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 L⁰(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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