Proximunalty in Orlicz-bochner Function Spaces

Abstract

It is the object of this paper is to study the proximinality of L Φ (I, Y ) in L Φ (I, X) for some class of Young's functions Φ, where I is the unit interval. We prove (among other results) that if Y is a separable proximinal subspace of X, then L Φ (I, Y ) is proximinal in L Φ (I, X).