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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Bibliographic Details
Published in:International journal of mathematics and mathematical sciences 2001-01, Vol.27 (1), p.39-44
Main Author: Mirmostafaee, S Alireza Kamel
Format: Article
Language:English
Online Access:Get full text
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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.
ISSN:0161-1712
1687-0425
DOI:10.1155/S0161171201005075