In this note, we present a generalization of Wigner's theorem. Let and be complex normed spaces with being smooth. We show that a surjective mapping satisfies where is a positive integer and is the set of the th roots of unity, if and only if there exists a phase function such that is a linear or an anti-linear isometry.

中文翻译：

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复杂光滑赋范空间中的维格纳定理

在这篇文章中，我们提出了维格纳定理的推广。设 和 是光滑的复杂赋范空间。我们证明，满射映射满足其中 是正整数并且是单位根的集合，当且仅当存在线性或反线性等距的相位函数。