ISOMETRIES OF THE UNITE SPHERE

Abstract

It is extended that DARYL TINGLEY's results about that isometries between the unit spheres of finite dimensional Banach spaces necessarily map antipodal points to antipodal points.Now, the results is obtained in strictly convex (or l1) spaces, i.e.: If X, Y are two strictly convex onto (or l1) spaces, and S(X), S(Y) are the unit spheres of X and Y respectively, f: S(X) → S (Y) is an isometry, then f (–x) = – f (x), for any x in S (X).