# Remarks on Isometries of Products of Linear Spaces

1 Equations d'evolution
SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
Abstract : Given two normed spaces $X$ , $Y$ , the aim of this paper is establish that the existence of an isomorphism isometric between $X \times R$ and $Y \times R$ is equivalent to the existence of an isometric isomorphism between $X$ and $Y$ , provided the norms satisfy an appropriate condition. By means of a counterexample, it is shown that this result fails for arbitrary norms even if $X = Y = R^2$.
Type de document :
Article dans une revue
Extracta Mathematicae, 2015, 30 (1), pp.1-13

https://hal-paris1.archives-ouvertes.fr/hal-01183199
Contributeur : Mohammed Bachir <>
Soumis le : jeudi 6 août 2015 - 16:33:26
Dernière modification le : lundi 27 novembre 2017 - 14:14:02

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• HAL Id : hal-01183199, version 1

### Citation

Mohammed Bachir. Remarks on Isometries of Products of Linear Spaces. Extracta Mathematicae, 2015, 30 (1), pp.1-13. 〈hal-01183199〉

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