Equilateral sets in infinite dimensional Banach spaces

S. K. Mercourakis; G. Vassiliadis

Equilateral sets in infinite dimensional Banach spaces

Functional Analysis 2013-04-25 v2 Metric Geometry

Authors: S. K. Mercourakis , G. Vassiliadis

Abstract

We show that every Banach space $X$ containing an isomorphic copy of $c_0$ has an infinite equilateral set and also that if $X$ has a bounded biorthogonal system of size $\alpha$ then it can be renormed so as to admit an equilateral set of equal size. If $K$ is any compact non metrizable space, then under a certain combinatorial condition on $K$ the Banach space $C(K)$ has an uncountable equilateral set.

Keywords

banach spaces banach algebras general topology

Cite

@article{arxiv.1111.2273,
  title  = {Equilateral sets in infinite dimensional Banach spaces},
  author = {S. K. Mercourakis and G. Vassiliadis},
  journal= {arXiv preprint arXiv:1111.2273},
  year   = {2013}
}

Comments

to appear in Proc. Am. Math. Soc. (9 pages, no figures)

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