Bulletin of the Australian Mathematical Society

Table of Contents - April 1999 - Volume 59, Issue 02  

Research Article

Linear isometries between spaces of functions of bounded variation

Jesuś Araujoa1

a1 Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Facultad de Ciencias, 39071 Santander, Spain e-mail: araujo@matesco.unican.es

Abstract

Given two subsets X and Y of xs211D each with at least two points, we describe the surjective linear isometries between the spaces of functions of bounded variation BV(X) and BV(Y): namely, if T : BV(X) → BV(Y) is such an isometry, then there exist α xs2208 xs2102, |α| = 1, and a monotonic bijective map h : Y → X such that (Tf)(y) = αf(h(y)) for every f xs2208 BV(X) and every y xs2208 Y.

(Received October 01 1998)