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arXiv · 1305.6750

Equilateral sets in uniformly smooth Banach spaces

D. Freeman·E. Odell·B. Sari·Th. Schlumprecht
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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 $i\neq j$.

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D. Freeman, E. Odell, B. Sari, Th. Schlumprecht. 2013-05-29. Equilateral sets in uniformly smooth Banach spaces. https://doi.org/10.1112/s0025579313000260

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