The Mazur–Ulam property for the space of complex null sequences

Abstract

ABSTRACTGiven an infinite set , we prove that the space of complex null sequences, , satisfies the Mazur–Ulam property, that is, for each Banach space X, every surjective isometry from the unit sphere of onto the unit sphere of X admits a (unique) extension to a surjective real linear isometry from to X. We also prove that the same conclusion holds for the finite-dimensional space .