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Journal Articles Extracta Mathematicae Year : 2015

Remarks on Isometries of Products of Linear Spaces

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Mohammed Bachir
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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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Dates and versions

hal-01183199 , version 1 (06-08-2015)

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  • HAL Id : hal-01183199 , version 1

Cite

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