Concerning the Hahn-Banach theorem

Holbrook, John A. R.

doi:10.1090/S0002-9939-1975-0370139-3

Concerning the Hahn-Banach theorem
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by John A. R. Holbrook PDF

Proc. Amer. Math. Soc. 50 (1975), 322-327 Request permission

Abstract:

We establish an intrinsic characterization for those normed spaces having the extension property that applies equally to spaces with real, complex, or quaternionic scalars. Nachbin’s characterization for real spaces via the binary intersection property follows as a special case. The method also yields a proof of the Hahn-Banach theorem that does not depend on the choice of scalar field.

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