Abstract

The purpose of this Note is to present an extension of the classical Jordan-von Neumann (JN) theorem [3] - which is recalled below - to the case of a normed space over the skew field IH of quaternions. It is known that this extension is valid in a more general framework (see [5], [6], [7], [8]), but our approach is based on elementary arguments only. So, this result may be of interest for students, applied researchers, etc. We think this extension could be applied to control theory, mechanics and other areas.