2005/08/17 by A K Mirmostafaee
Mathematics · #math.FA #msc:46B20 #msc:54E99 #msc:54H05
published as Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2, May 2005, pp. 201-207 · 7 pages, no figures, no tables
arxiv created 2005/08/17 · arxiv updated 2009/12/01
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.