Norms on C1 ([0, 1]) and their isometries

Abstract

We present a unified framework to study isometries, with respect to various norms, on C 1 ([0, 1]), the space of continuously first differentiable functions on the unit interval [0, 1]. We also discuss continuous deformations of isometry groups induced by perturbations of norms on C 1 ([0, 1])