
Journal of Convex Analysis 21 (2014), No. 1, 179188 Copyright Heldermann Verlag 2014 Some More Applications of the HahnBanach Theorem Francisco Javier GarcíaPacheco 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 HahnBanach 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 HahnBanach Separation Theorem is provided without involving the Axiom of Choice. Keywords: Equivalent norm, dual norm, HahnBanach, Axiom of Choice. MSC: 46B20 [ Fulltextpdf (119 KB)] for subscribers only. 