Dual Clifford modules

Abstract

A relationship between the space dual to the realification of a module over a Clifford algebra and the realification of the dual of this module is established. This relationship is completely analogous to a similar classical relationship between the space dual to the realification of a complex vector space and the realification of the dual of the given space. On the basis of this relationship, questions concerning extension of linear functionals on Clifford modules, in particular, a counterpart of the Hahn–Banach theorem, are considered.