Equilateral sets in uniformly smooth Banach spaces

D. Freeman, E. Odell, B. Sari, Th. Schlumprecht

Published 2013-05-29Version 1

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 $i\neq j$.