Resumen de Remarks on Isometries of Products of Linear Spaces

Mohammed Bachir

• 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.