Article contents
EQUILATERAL SETS IN UNIFORMLY SMOOTH BANACH SPACES
Published online by Cambridge University Press: 02 January 2014
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
$\lambda \gt 0$ and an infinite sequence
$\mathop{({x}_{i} )}\nolimits_{i= 1}^{\infty } \subset X$ such that
$\Vert {x}_{i} - {x}_{j} \Vert = \lambda $ for all
$i\not = j$.
MSC classification
- Type
- Research Article
- Information
- Copyright
- Copyright © University College London 2014
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:72705:20160415013550641-0011:S0025579313000260_inline7.gif?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:69580:20160415013550641-0011:S0025579313000260_inline8.gif?pub-status=live)
- 6
- Cited by