A note on nonfragmentability of Banach spaces (Q1599701)
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scientific article; zbMATH DE number 1751229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A note on nonfragmentability of Banach spaces |
scientific article; zbMATH DE number 1751229 |
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A note on nonfragmentability of Banach spaces (English)
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14 March 2003
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The author uses the Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space \(X\) with tree-completeness property contains a disjoint sequences of clopen sets, then (\(C(X)\), weak) is not fragmented by any metric which is stronger than weak topology (Theorem 2.4). In particular, \(C(X)\) does not admit any equivalent locally uniformly convex renorming (Corollary 2.5).
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fragmentable topological space
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winning strategy
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locally uniformly convex norm
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Kenderov-Moors characterization
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tree-completeness
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0.8774603605270386
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0.8751370310783386
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0.803488552570343
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0.7992857694625854
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