Equilateral sets in uniformly smooth Banach spaces

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 $\Vert x_i-x_j\Vert =\lambda$ for all $i\ne j$.

11 pages

References in corpus (1)

• A lower bound for the equilateral number of normed spaces

Cited by in corpus (2)

• Combinatorial distance geometry in normed spaces
• A note on symmetric separation in Banach spaces