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

Ioffe, A. D.

doi:10.1090/S0002-9939-1981-0612725-1

A new proof of the equivalence of the Hahn-Banach extension and the least upper bound properties
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Proc. Amer. Math. Soc. 82 (1981), 385-389 Request permission

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.

References

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On semi-ordered linear spaces and their applications to the theory of linear operators

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