A Note on the Extension of Ε-Isometries on the Unit Sphere of Banach Spaces

Abstract

Let X, Y be Banach spaces, S X and S Y be the unit sphere of X and Y, respectively. Let f 0 : S X -+ S Y be epsilon- isometry for some epsilon >= 0. In this paper, we show that there is an extension f : X -+ Y of f 0 such that f is linear.