Best ∞-simultaneous approximation in Banach lattice function spaces

Abstract

Let X be a conditional complete Banach lattice space. We are concerned with the proximinality problem for best simultaneous approximations to two functions in the K\"{o}the Bochner function spaces in the $l_{\infty}$sum sense. This characterization can be considered as a generalization of some analogous theorems concerning the Orlicz Bochner spaces and Lp Bochner spaces.