Best ∞-simultaneous approximation in Banach lattice function spaces

摘要

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.