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A note on convex renorming and fragmentability

A K Mirmostafaee
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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.

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A K Mirmostafaee. 2005-08-17. A note on convex renorming and fragmentability. https://arxiv.org/abs/math/0508311

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