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arXiv · 1801.02002

Antipodal sets in infinite dimensional Banach spaces

Eftychios Glakousakis·Sophocles Mercourakis
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Abstract

The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ and a constant $d>1$, satisfying the property that for every $x,y\in S$ with $x\neq y$ there exists $f\in B_{X^*}$ such that $d\leq f(x)-f(y)$ and $f(y)\leq f(z)\leq f(x)$, for all $z\in S$.

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Eftychios Glakousakis, Sophocles Mercourakis. 2018-01-06. Antipodal sets in infinite dimensional Banach spaces. https://arxiv.org/abs/1801.02002

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