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Minimal ball-coverings in Banach spaces and their application

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Cheng L., Cheng Q., Shi H.

Studia Mathematica

2009

tom 192

nr 1

15-27

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.

Ograniczanie wyników

1 Studia Mathematica

1 Cheng L.

1 Cheng Q.

1 Shi H.

1 2009

Wyniki wyszukiwania

Minimal ball-coverings in Banach spaces and their application