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A note on nonfragmentability of Banach spaces

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  • S. Alireza Kamel Mirmostafaee

Abstract

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.

Suggested Citation

  • S. Alireza Kamel Mirmostafaee, 2001. "A note on nonfragmentability of Banach spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 27, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:674640
    DOI: 10.1155/S0161171201005075
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