Real-Linear Isometries on Spaces of Functions of Bounded Variation

摘要

Let X and Y be subsets of the real line with at least two points. We study the surjective real-linear isometries between the spaces of functions of bounded variation on X and Y with respect to the supremum norm and the complete norm , where denotes the total variation of a function. Additively norm preserving maps between these spaces are also characterized as a corollary.