A note on nonfragmentability of Banach spaces
We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space X with the 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. In particular, C(X) does not...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201005075 |
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| Summary: | We use Kenderov-Moors characterization of fragmentability to
show that if a compact Hausdorff space X with the
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. In particular,
C(X) does not admit any equivalent locally uniformly
convex renorming. |
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| ISSN: | 0161-1712 1687-0425 |