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Proceedings of the American Mathematical Society

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A new proof of the equivalence of the Hahn-Banach extension and the least upper bound properties

Author: A. D. Ioffe
Journal: Proc. Amer. Math. Soc. 82 (1981), 385-389
MSC: Primary 46A22; Secondary 46A40
MathSciNet review: 612725
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Abstract: The paper contains a new proof of the fact that the Hahn-Banach majorized extension theorem for linear operators is valid iff the range ordered space is conditionally complete. The proof is based on quite different principles than the original proof of Bonnice, Silverman and To. The key element is a reformulation of the extension problem in terms of linear selections of special convex-valued mappings called fans.

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Keywords: Ordered vector space, sublinear operator, Hahn-Banach extension, convexvalued mapping, fan, binary intersection property, least upper bound, conditionally complete order
Article copyright: © Copyright 1981 American Mathematical Society

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