English

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.

Keywords

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