Given two subsets X and Y of the real line with at least two points, we apply results on surjective linear isometries between Banach spaces of all functions of bounded variation BV(X) and BV(Y) to show that every 2-local isometry \(T:BV(X)\longrightarrow BV(Y)\) is a constant multiple of an isometric linear algebra isomorphism. Moreover, similar results are given for the closed subspaces of BV(X) and BV(Y) consisting of all continuous (resp. absolutely continuous) functions when X and Y are compact.

中文翻译：

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有界变化函数的空间之间的2-局部等距

给定实线的两个子集X和Y至少有两个点，我们将结果应用于有界变化BV（X）和BV（Y）的所有函数的Banach空间之间的射影线性等距，以表明每个2局部等距\ （T：BV（X）\ longrightarrow BV（Y）\）是等距线性代数同构的常数倍。此外，当X和Y紧凑时，对BV（X）和BV（Y）的闭合子空间给出的相似结果也包括所有连续（分别是绝对连续）函数。