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Remarks on Isometries of Products of Linear Spaces

Mohammed Bachir 1
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 $X = Y = R^2$.
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Submitted on : Thursday, August 6, 2015 - 4:33:26 PM
Last modification on : Wednesday, January 26, 2022 - 3:10:52 PM


  • HAL Id : hal-01183199, version 1



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



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