Isometries OF C(n)[0, 1]

Abstract

By C(n)[0, 1] (henceforth denoted by C(n)) we denote the Banach algebra of complex valued n times continuously differentiable functions on [0, 1] with norm given by an isometry of C(n)we mean a norm-preserving linear map of C(n)onto itself.The purpose of this article is to describe the isometries of C(n)) for any positive integer n. More precisely, we show that any isometry of C(n)) is induced by a point map of the interval [0, 1] onto itself . © 1981, University of California, Berkeley. All Rights Reserved.