On isometries of Product of normed linear spaces

Mohammed Bachir (1)

1 Equations d'evolution

We give a condition on norms under which two vector normed spaces $X$ and $Y$ are isometrically isomorphic if and only if $X\times \R$ and $Y\times \R$ are isometrically isomorphic. We also prove that this result fail for arbitrary norms even if $X=Y=\R^2$ by building a generic counterexamples.

Domaines: Analyse fonctionnelle [math.FA]

Mohammed Bachir. On isometries of Product of normed linear spaces. 2014. ⟨hal-01086201⟩