Ball‐Covering Property in Uniformly Non‐l3(1) Banach Spaces and Application

Shaoqiang Shang and Yunan Cui

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: This paper shows the following. (1) X is a uniformly non‐l3(1) space if and only if there exist two constants α, β > 0 such that, for every 3‐dimensional subspace Y of X, there exists a ball‐covering 𝔅 of Y with c(𝔅) = 4 or 5 which is α‐off the origin and r(𝔅) ≤ β. (2) If a separable space X has the Radon‐Nikodym property, then X* has the ball‐covering property. Using this general result, we find sufficient conditions in order that an Orlicz function space has the ball‐covering property.

Date: 2013
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https://doi.org/10.1155/2013/873943

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:873943

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