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
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.
[ Fulltext-pdf (119 KB)] for subscribers only.