Minimal ball-coverings in Banach spaces and their application

• Autorzy: Lixin Cheng , Qingjin Cheng , Huihua Shi
• Języki publikacji: 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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 58C20: Differentiation theory (Gateaux, Fr\'echet, etc.)
• 46T20: Continuous and differentiable maps

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 192
• Numer: 1
• Strony: 15-27

Daty

wydano

2009

Twórcy

autor

Lixin Cheng

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

autor

Qingjin Cheng

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

autor

Huihua Shi

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

Identyfikatory

DOI

10.4064/sm192-1-2