Extension of isometries between the unit spheres of normed space \(E\) and \(C(\Omega)\) (Q882754)
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scientific article; zbMATH DE number 5156879
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of isometries between the unit spheres of normed space \(E\) and \(C(\Omega)\) |
scientific article; zbMATH DE number 5156879 |
Statements
Extension of isometries between the unit spheres of normed space \(E\) and \(C(\Omega)\) (English)
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24 May 2007
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For any compact metric space \(\Omega\) and a real Banach space \(E\), the authors show that any surjective isometry between the unit spheres of \(C(\Omega)\) and \(E\) has an extension to a linear isometry between the spaces.
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surjective isometry of unit sphere
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linear isometry
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space of continuous functions
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Tingley's problem
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0.9625616
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0.9605067
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0.95841074
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0.94263035
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0.9347489
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