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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1832568377320669184 |
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| author | S. Alireza Kamel Mirmostafaee |
| author_facet | S. Alireza Kamel Mirmostafaee |
| author_sort | S. Alireza Kamel Mirmostafaee |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-94a31d50542b4ed7a5b97cf545f5bc70 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-94a31d50542b4ed7a5b97cf545f5bc702025-02-03T00:59:11ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01271394410.1155/S0161171201005075A note on nonfragmentability of Banach spacesS. Alireza Kamel Mirmostafaee0Department of Mathematics, Damghan College of Sciences, P.O. Box 364, Damghan 36715, IranWe 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.http://dx.doi.org/10.1155/S0161171201005075 |
| spellingShingle | S. Alireza Kamel Mirmostafaee A note on nonfragmentability of Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | A note on nonfragmentability of Banach spaces |
| title_full | A note on nonfragmentability of Banach spaces |
| title_fullStr | A note on nonfragmentability of Banach spaces |
| title_full_unstemmed | A note on nonfragmentability of Banach spaces |
| title_short | A note on nonfragmentability of Banach spaces |
| title_sort | note on nonfragmentability of banach spaces |
| url | http://dx.doi.org/10.1155/S0161171201005075 |
| work_keys_str_mv | AT salirezakamelmirmostafaee anoteonnonfragmentabilityofbanachspaces AT salirezakamelmirmostafaee noteonnonfragmentabilityofbanachspaces |