Vol. 94, No. 1, 1981

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ISSN: 0030-8730
Isometries of C(n)[0, 1]

V. D. Pathak

Vol. 94 (1981), No. 1, 211–222
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

            n∑   |f(r)(x)|          (n)
∥f∥ = xs∈u[p0,1](  (  r!   )) for f ∈ C  .
r=0

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.

Mathematical Subject Classification 2000
Primary: 46E15
Milestones
Received: 2 February 1979
Revised: 27 April 1979
Published: 1 May 1981
Authors
V. D. Pathak