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

Abstract EN

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 ? of Y with c(?)=4 or 5 which is α-off the origin and r(?)≤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.