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Real-Linear Isometries on Spaces of Functions of Bounded Variation

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Abstract

Let X and Y be subsets of the real line with at least two points. We study the surjective real-linear isometries \({T:BV(X)\longrightarrow BV(Y)}\) between the spaces of functions of bounded variation on X and Y with respect to the supremum norm \({\|\cdot\|_\infty}\) and the complete norm \({\|\cdot\|:=\max(\|\cdot\|_\infty,\mathcal{V}(\cdot))}\), where \({\mathcal{V}(\cdot)}\) denotes the total variation of a function. Additively norm preserving maps between these spaces are also characterized as a corollary.

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  1. Department of Mathematics, K.N. Toosi University of Technology, Tehran, 16315-1618, Iran

    Maliheh Hosseini

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  1. Maliheh Hosseini
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Hosseini, M. Real-Linear Isometries on Spaces of Functions of Bounded Variation. Results. Math. 70, 299–311 (2016). https://doi.org/10.1007/s00025-015-0489-4

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  • DOI: https://doi.org/10.1007/s00025-015-0489-4

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