EQUILATERAL SETS IN UNIFORMLY SMOOTH BANACH SPACES. Issue 1 (2nd January 2014) - Freeman, D.; Odell, E.; Sari, B.; Schlumprecht, Th.
Abstract: Let X be an infinite‐dimensional uniformly smooth Banach space. We prove that X contains an infinite equilateral set. That is, there exist a constant λ > 0 and an infinite sequence ( x i ) i = 1 ∞ ⊂ X such that ∥ x i ‐ x j ∥ = λ for all i ≠ j .