A note on convex renorming and fragmentability
Functional Analysis
2007-05-23 v1
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.
Cite
@article{arxiv.math/0508311,
title = {A note on convex renorming and fragmentability},
author = {A K Mirmostafaee},
journal= {arXiv preprint arXiv:math/0508311},
year = {2007}
}
Comments
7 pages, no figures, no tables