[Banach] Abstract of a paper by A K Mirmostafaee

This is an announcement for the paper "A note on convex renorming and fragmentability" by A K Mirmostafaee.

Abstract: 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.

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B20, 54E99, 54H05 Citation: Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 2, May 2005,

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