Uniform Kadec-Klee Property in Banach lattices

Fouad Chaatit; M. Khamsi

Uniform Kadec-Klee Property in Banach lattices

Functional Analysis 2009-09-25 v1

Authors: Fouad Chaatit , M. Khamsi

Abstract

We prove that a Banach lattice $X$ which does not contain the $l^n_{\infty}$ -uniformly has an equivalent norm which is uniformly Kadec-Klee for a natural topology $\tau$ on $X$ . In case the Banach lattice is purely atomic, the topology $\tau$ is the coordinatewise convergence topology.

Keywords

Banach lattice uniform Kadec-Klee property equivalent norm coordinatewise convergence purely atomic

Cite

@article{arxiv.math/9406209,
  title  = {Uniform Kadec-Klee Property in Banach lattices},
  author = {Fouad Chaatit and M. Khamsi},
  journal= {arXiv preprint arXiv:math/9406209},
  year   = {2009}
}

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