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• # Artykuł - szczegóły

## Studia Mathematica

2009 | 192 | 1 | 15-27

## Minimal ball-coverings in Banach spaces and their application

EN

### Abstrakty

EN
By a ball-covering 𝓑 of a Banach space X, we mean a collection of open balls off the origin in X and whose union contains the unit sphere of X; a ball-covering 𝓑 is called minimal if its cardinality $𝓑^{#}$ is smallest among all ball-coverings of X. This article, through establishing a characterization for existence of a ball-covering in Banach spaces, shows that for every n ∈ ℕ with k ≤ n there exists an n-dimensional space admitting a minimal ball-covering of n + k balls. As an application, we give a new characterization of superreflexive spaces in terms of ball-coverings. Finally, we show that every infinite-dimensional Banach space admits an equivalent norm such that there is an infinite-dimensional quotient space possessing a countable ball-covering.

15-27

wydano
2009

### Twórcy

autor
• Department of Mathematics, Xiamen University, Xiamen 361005, China
autor
• Department of Mathematics, Xiamen University, Xiamen 361005, China
autor
• Department of Mathematics, Xiamen University, Xiamen 361005, China