Extensions of functionals on octonionic linear spaces
type: Item
instance of: scholarly article
title: Extensions of functionals on octonionic linear spaces
zbMATH Open document ID: 0675.46039
DOI: 10.1007/BF01951570
author: J. L. Lewis
published in: Acta Mathematica Hungarica
publication date: 1988-01-01T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 46S10
Mathematics Subject Classification ID: 46A22
zbMATH DE Number: 4105634
zbMATH Keywords: Hahn-Banach extension theorem for normed spaces over the valued field 0 of the octonions
zbMATH Keywords: Hahn-Banach extension theorem for quaternionic normed
MaRDI profile type: Publication
cites work: Hilbert space with non-associative scalars. I
cites work: Extensions of functionals on complex linear spaces
full work available at URL: https://doi.org/10.1007/bf01951570
OpenAlex ID: W2069372131
description: scientific article; zbMATH DE number 4105634