Ball proximinality in Banach spaces

摘要

In this paper we study the notion of ball proximinality. We exhibit several classes of Banach spaces that are ball proximinal. We show that the unit ball of an Al-ideal is proximinal in the unit ball of the whole space. We also define a stronger notion of ball proximinality and show that in a locally uniformly convex space, the unit ball is strongly ball proximinal. We show that strong proximinality does not imply ball proximinality. We also consider ball proximinality for spaces of vector-valued continuous and Bochner integrable functions.