The Kreps-Yan theorem for L^∞

2004/12/31 by Dmitry B. Rokhlin, Rokhlin, Dmitry B.
Mathematics · #46B40 #46E30 #Advanced Algebra and Geometry #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #advanced mathematical theories #math.FA #msc:46B40 #msc:46E30

paper · pdf · doi:10.48550/arxiv.math/0412551

8 pages

arxiv created 2004/12/31 · openalex publication_date 2004/12/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the following version of the Kreps-Yan theorem. For any norm closed convex cone C⊂ L^∞ such that C∩ L₊^∞=\0\ and C⊃ -L₊^∞, there exists a strictly positive continuous linear functional, whose restriction on C is non-positive. The proof uses some tools from convex analysis in contrast to the case of a weakly Lindelöf Banach space, where such approach is not needed.

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