Antipodal sets in infinite dimensional Banach spaces

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 $x\ne y$ there exists $f\in B_{X^{\ast }}$ such that $d\le f(x)-f(y)$ and $f(y)\le f(z)\le f(x)$, for all $z\in S$.

arXiv comment15 pages, to appear in Bulletin of the Hellenic Mayhematical Society

Cited by in corpus (1)

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