On non-surjective coarse isometries between Banach spaces

AbstractAssume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that ifthen there is a linear isometry U : X → Y so thatwhere is defined byRepresentation properties of coarse isometries in free ultrafilter limits on are also discussed.