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Generalization of the Arrow–Barankin–Blackwell Theorem in a Dual Space Setting

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Abstract

In this note, we provide general sufficient conditions under which, if F is a compact [resp. w*-compact] subset of the topological dual Y* of a nonreflexive normed space Y partially ordered by a closed convex pointed cone K, then the set of points in F that can be supported by strictly positive elements in the canonical embedding of Y in Y** is norm dense [resp. w*-dense] in the efficient [maximal] point set of F. This result gives an affirmative answer to the conjecture proposed by Gallagher (Ref. 19), and also generalizes the results stated in Ref. 19 and some space specific results given in Refs. 17, 18, and 11.

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Author notes

  1. W. Song (Lecturer)

    Present address: Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland

Authors and Affiliations

  1. Department of Mathematics, Harbin Normal University, Harbin, China;

    W. Song (Lecturer)

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  1. W. Song
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Song, W. Generalization of the Arrow–Barankin–Blackwell Theorem in a Dual Space Setting. Journal of Optimization Theory and Applications 95, 225–230 (1997). https://doi.org/10.1023/A:1022647831434

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  • DOI: https://doi.org/10.1023/A:1022647831434

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