This is an announcement for the paper "Uncountable sets of unit vectors that are separated by more than 1" by Tomasz Kania and Tomasz Kochanek.

Abstract: Let $X$ be a Banach space. We study the circumstances under which there exists an uncountable set $\mathcal A\subset X$ of unit vectors such that $|x-y|>1$ for distinct $x,y\in \mathcal A$. We prove that such a set exists if $X$ is quasi-reflexive and non-separable; if $X$ is additionally super-reflexive then one can have $|x-y|\geqslant 1+\varepsilon$ for some $\varepsilon>0$ that depends only on $X$. If $K$ is a compact, Hausdorff space, then $X=C(K)$ contains such a set of cardinality equal to the density of $X$; this solves a problem left open by S. K. Mercourakis and G. Vassiliadis.

Archive classification: math.FA math.MG

Remarks: 17 pp

Submitted from: tomasz.marcin.kania@gmail.com

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1503.08166

or

http://arXiv.org/abs/1503.08166