Quaternion normed space with isometry group ℤ2

Quaternion normed space with isometry group ℤ2

In a finite-dimensional linear space over the quaternion field, we construct a norm with the following property. Any linear isometry is one of the two transformations x ↦ x and x ↦ − x .

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Veröffentlicht in:Functional analysis and its applications 2008, Vol.42 (3), p.239-241
Hauptverfasser: Ismagilov, R. S., Lyubich, Yu. I.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Functional Analysis
Mathematics
Mathematics and Statistics
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung:In a finite-dimensional linear space over the quaternion field, we construct a norm with the following property. Any linear isometry is one of the two transformations x ↦ x and x ↦ − x .
ISSN:0016-2663
1573-8485
DOI:10.1007/s10688-008-0036-0