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A Mazur–Ulam theorem in non-Archimedean normed spaces. (English) Zbl 1160.46049
Summary: The classical Mazur–Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly convex normed spaces.

MSC:
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
47S10 Operator theory over fields other than \(\mathbb{R}\), \(\mathbb{C}\) or the quaternions; non-Archimedean operator theory
26E30 Non-Archimedean analysis
12J25 Non-Archimedean valued fields
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