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Journal of Convex Analysis 21 (2014), No. 1, 179--188
Copyright Heldermann Verlag 2014

Some More Applications of the Hahn-Banach Theorem

Francisco Javier García-Pacheco
Dept. of Mathematics, University of Cadiz, Puerto Real 11510, Spain

Daniele Puglisi
Dept. of Mathematics, University of Catania, Catania 95125, Italy

Gusti van Zyl
Dept. of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa

We give a new proof of the fact that equivalent norms on subspaces can be extended. This new proof is based on the Hahn-Banach Extension Theorem. We also give new characterizations for an equivalent norm on a dual space to be a dual norm. Finally, a new proof of a particular case of the Hahn-Banach Separation Theorem is provided without involving the Axiom of Choice.

Keywords: Equivalent norm, dual norm, Hahn-Banach, Axiom of Choice.

MSC: 46B20

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