The isometric extension of an into mapping from the unit sphere s[l(Γ)] to the unit sphere S(E)

This is such a article to consider an “into” isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition (using the Krein-Milman property) under which an into-isometric mapping from the unit sphere of l(Γ) to the unit sphere of a normed space E can be linearly isometric extended.