Remarks on Isometries of Products of Linear Spaces

Mohammed Bachir ^[1]
1. [1] Université Paris, París. France
Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 30, Nº 1, 2015, págs. 1-13
Idioma: inglés
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Resumen
- Given two normed spaces X, Y , the aim of this paper is establish that the existence of an isomorphism isometric between X x R and Y x 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 = R2.