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arXiv · 1111.2273

Equilateral sets in infinite dimensional Banach spaces

S. K. Mercourakis·G. Vassiliadis
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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.

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S. K. Mercourakis, G. Vassiliadis. 2011-11-09. Equilateral sets in infinite dimensional Banach spaces. https://arxiv.org/abs/1111.2273

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