Equilateral sets in uniformly smooth Banach spaces

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

doi:10.1112/S0025579313000260

Equilateral sets in uniformly smooth Banach spaces

Functional Analysis 2019-02-20 v1

Authors: 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 $i\neq j$ .

Keywords

banach spaces banach space properties

Cite

@article{arxiv.1305.6750,
  title  = {Equilateral sets in uniformly smooth Banach spaces},
  author = {D. Freeman and E. Odell and B. Sari and Th. Schlumprecht},
  journal= {arXiv preprint arXiv:1305.6750},
  year   = {2019}
}

Comments

11 pages

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