# 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 $X = Y = R^2$.
Document type :
Journal articles
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https://hal-paris1.archives-ouvertes.fr/hal-01183199
Contributor : Mohammed Bachir <>
Submitted on : Thursday, August 6, 2015 - 4:33:26 PM
Last modification on : Sunday, January 19, 2020 - 6:38:38 PM

### Identifiers

• 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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