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Linear isometries between spaces of functions of bounded variation

Published online by Cambridge University Press:  17 April 2009

Jesuś Araujo
Jesuś Araujo
Affiliation:
Departamento de Matemáticas, Estadística y Computación, Universidad de Cantabria, Facultad de Ciencias, 39071 Santander, Spain e-mail: [email protected]
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Abstract

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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
Bulletin of the Australian Mathematical Society , Volume 59 , Issue 2 , April 1999 , pp. 335 - 341
Copyright
Copyright © Australian Mathematical Society 1999

References

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