Isometries of normed spaces (Q2773365)
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scientific article; zbMATH DE number 1709955
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Isometries of normed spaces |
scientific article; zbMATH DE number 1709955 |
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Isometries of normed spaces (English)
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21 February 2002
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Banach-Mazur theorem
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isometry
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affine
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By a classical result of Mazur and Ulam a surjective isometry of a real normed space is affine. The authors obtain the same conclusion by replacing the surjectivity condition by a weaker one; namely, an isometry \(f: X\to Y\) is affine if for every unit vector \(y\in Y\) there exist \(a,b\in X\) and \(s\in \mathbb R\) such that \(\|y-s(f(a)-f(b))\|<1/2\).
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