Kadec norms on spaces of continuous functions

Max Burke; Wieslaw Kubis; Stevo Todorcevic

Kadec norms on spaces of continuous functions

Functional Analysis 2012-10-23 v1

Authors: Max Burke , Wieslaw Kubis , Stevo Todorcevic

Abstract

We study the existence of pointwise Kadec renormings for Banach spaces of the form $C(K)$ . We show in particular that such a renorming exists when $K$ is any product of compact linearly ordered spaces, extending the result for a single factor due to Haydon, Jayne, Namioka and Rogers. We show that if $C(K_1)$ has a pointwise Kadec renorming and $K_2$ belongs to the class of spaces obtained by closing the class of compact metrizable spaces under inverse limits of transfinite continuous sequences of retractions, then $C(K_1\times K_2)$ has a pointwise Kadec renorming. We also prove a version of the three-space property for such renormings.

Keywords

banach spaces fixed point in banach spaces banach space properties

Cite

@article{arxiv.math/0312013,
  title  = {Kadec norms on spaces of continuous functions},
  author = {Max Burke and Wieslaw Kubis and Stevo Todorcevic},
  journal= {arXiv preprint arXiv:math/0312013},
  year   = {2012}
}

Comments

22 pages

Kadec norms on spaces of continuous functions

Abstract

Keywords

Cite

Comments

Related papers