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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Concerning the Hahn-Banach theorem


Author: John A. R. Holbrook
Journal: Proc. Amer. Math. Soc. 50 (1975), 322-327
MSC: Primary 46B05
MathSciNet review: 0370139
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0370139-3
PII: S 0002-9939(1975)0370139-3
Keywords: Hahn-Banach theorem, complex normed spaces, extension property
Article copyright: © Copyright 1975 American Mathematical Society