Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Francisco Javier García-Pacheco

Dept. of Mathematics, University of Cadiz, Puerto Real 11510, Spain

garcia.pacheco@uca.es

Gusti van Zyl

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

gusti.vanzyl@up.ac.za

Keywords

  • Equivalent norm
  • dual norm
  • Hahn-Banach
  • Axiom of Choice

Mathematics Subject Classification

46B20

Suggested citation

F. J. García-Pacheco, D. Puglisi, G. van Zyl. “Some More Applications of the Hahn-Banach Theorem.” Journal of Convex Analysis 21 (2014), No. 1, 179–188.

Copyright Banach Press 2014