Article contents
Linear isometries between spaces of functions of bounded variation
Published online by Cambridge University Press: 17 April 2009
Abstract
Given two subsets X and Y of ℝ 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 ∈ ℂ, |α| = 1, and a monotonic bijective map h : Y → X such that (Tf)(y) = αf(h(y)) for every f ∈ BV(X) and every y ∈ Y.
- Type
- Research Article
- Information
- Copyright
- Copyright © Australian Mathematical Society 1999
References
- 7
- Cited by