Some characterizations of finite-dimensional Hilbert spaces (Q1269612)
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scientific article; zbMATH DE number 1215680
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some characterizations of finite-dimensional Hilbert spaces |
scientific article; zbMATH DE number 1215680 |
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Some characterizations of finite-dimensional Hilbert spaces (English)
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1998
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The main result of the paper is: if each extreme point of the unit ball of the space of operators on a finite-dimensional normed linear space \(X\) is an isometry, then the space \(X\) is isometric to a Hilbert space (of the corresponding dimension). The converse statement is well-known. The proof is based on the fact that finite-dimensional spaces with transitive norms are Hilbertian.
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extreme point of the unit ball
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finite-dimensional spaces with transitive norms
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