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
garcia.pacheco@uca.es
Daniele Puglisi
Dept. of Mathematics, University of Catania, Catania 95125, Italy
dpuglisi@dmi.unict.it
Gusti van Zyl
Dept. of Mathematics and Applied Mathematics, University of Pretoria, 0002 Pretoria, South Africa
gusti.vanzyl@up.ac.za
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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