Kreps-Yan theorem for Banach ideal spaces

2008/04/14 by Dmitry B. Rokhlin, Rokhlin, Dmitry B. · 1 citation
Computer Science · Mathematics · #46B42 #46E30 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Optimization and Variational Analysis #math.FA #msc:46B42 #msc:46E30

paper · pdf · doi:10.48550/arxiv.0804.2075

6 pages

arxiv created 2008/04/14 · openalex publication_date 2008/04/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a closed convex cone in a Banach ideal space X on a measurable space with a σ-finite measure. We prove that conditions C∩ X₊=\0\ and C⊃ -X₊ imply the existence of a strictly positive continuous functional on X, whose restriction to C is non-positive.

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