arXiv math/05083112005-08-17math.FA

A note on convex renorming and fragmentability

A K Mirmostafaee

备注：: 7 pages, no figures, no tables
发表信息：: Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2, May 2005, pp. 201-207

英文摘要：

Using the game approach to fragmentability, we give new and simpler proofs of the following known results: (a) If the Banach space admits an equivalent Kadec norm, then its weak topology is fragmented by a metric which is stronger than the norm topology. (b) If the Banach space admits an equivalent rotund norm, then its weak topology is fragmented by a metric. (c) If the Banach space is weakly locally uniformly rotund, then its weak topology is fragmented by a metric which is stronger than the norm topology.

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