This is an announcement for the paper "Equilateral sets in uniformly smooth Banach spaces" by D. Freeman, E. Odell, B. Sari, and Th. Schlumprecht.

Abstract: Let $X$ be an infinite dimensional uniformly smooth Banach space. We prove that $X$ contains an infinite equilateral set. That is, there exists a constant $\lambda>0$ and an infinite sequence $(x_i)_{i=1}^\infty\subset X$ such that $|x_i-x_j|=\lambda$ for all $i\neq j$.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B04

Remarks: 11 pages

Submitted from: dfreema7@slu.edu

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

http://front.math.ucdavis.edu/1305.6750

or

http://arXiv.org/abs/1305.6750