Extensions of functionals on octonionic linear spaces
The author proves the Hahn-Banach extension theorem for normed spaces over the valued field 0 of the octonions. Since every octonian \(a=a_ 0+a_ 1e_ 1+....+a_ 7e_ 7\) has a representation \(a=q_ 0+e_ 3q_ 1\), where \(q_ 0\) and \(q_ 1\) are quaternions, the proof of the theorem consists in reducing the problem to the Hahn-Banach extension theorem for quaternionic normed spaces proved by \textit{G. A. Sukhomlinov} [Mat. Sb. 3, 353-358 (1938; Zbl 0019.16905)].
Hahn-Banach extension theorem for normed spaces over the valued field 0 of the octonions
Hahn-Banach extension theorem for quaternionic normed
scientific article; zbMATH DE number 4105634