In this paper we give a complete description of surjective linear isometries between Banach spaces of absolutely continuous functions on arbitrary (not necessarily compact) subsets of the real line with respect to the sum-norm. We also use this description to study approximate local isometries and approximate 2-local isometries on these spaces. In particular, we present generalizations of all known results concerning such isometries, and obtain the reflexivity and 2-reflexivity of the isometry group of absolutely continuous function spaces in a noncompact framework.

中文翻译：

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绝对连续函数空间关于和范数的等距

在本文中，我们给出了关于和范数的实线任意（不一定是紧凑）子集上绝对连续函数的 Banach 空间之间的满射线性等距的描述。我们还使用此描述来研究这些空间上的近似局部等距和近似 2-局部等距。特别是，我们提出了有关此类等距的所有已知结果的概括，并获得了非紧框架中绝对连续函数空间的等距群的自反性和2-自反性。