This is an announcement for the paper "Equilateral sets in infinite dimensional Banach spaces" by S. K. Mercourakis and 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.

Archive classification: math.FA math.MG

Mathematics Subject Classification: Primary 46B20, Secondary 46B26, 46B04

Remarks: 15 pages, no figures

Submitted from: smercour@math.uoa.gr

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

http://front.math.ucdavis.edu/1111.2273

or

http://arXiv.org/abs/1111.2273