TREATMENT OF THE FIELDS HAVING THE HAHN-BANACH PROPERTY

Abstract

In this paper we deal with a classical theorem in functional analysis, the Hahn-Banach Theorem, in the general case when the scalars are vectors of R^n; n>1. For this purpose, the Hahn-Banach property for an arbitrary valued field is defined and the case when the scalar field is the quaternions field H(R4) is treated. The finding of fields L fulfulling the Hahn-Banach property represents an interesting problem. Certain remarks in the case when the field is with zero characteristic are presented.