Ismagilov, R. S.; Lyubich, Yu. I. Quaternion normed space with isometry group \(\mathbb Z_{2}\). (English) Zbl 1170.46314 Funct. Anal. Appl. 42, No. 3, 239-241 (2008); translation from Funkts. Anal. Prilozh. 42, No. 3, 90-92 (2008). In a finite-dimensional linear space over the quaternions, the authors construct a norm with the property that any linear isometry is one of the two transformations \(x\mapsto x\) and \(x\mapsto -x\). Reviewer: Aleksandar Perović (Berlin) MSC: 46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis 46B04 Isometric theory of Banach spaces Keywords:quaternion normed space; isometry PDFBibTeX XMLCite \textit{R. S. Ismagilov} and \textit{Yu. I. Lyubich}, Funct. Anal. Appl. 42, No. 3, 239--241 (2008; Zbl 1170.46314); translation from Funkts. Anal. Prilozh. 42, No. 3, 90--92 (2008) Full Text: DOI References: [1] Yu. I. Lyubich, Sibirsk. Mat. Zh., 11:2 (1970), 359–369. [2] Yu. I. Lyubich and O. A. Shatalova, Algebra i Analiz, 16:1 (2004), 15–32. [3] Yu. I. Lyubich and L. N. Vaserstein, Geom. Dedicata, 47:3 (1993), 327–362. · Zbl 0785.52002 · doi:10.1007/BF01263664 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.