Banach Lattices of Continuous Banach Lattice-Valued Functions

This paper studies the Banach lattice structure of some spaces of continuous functions taking values in a Banach lattice. We determine when they satisfy various kinds of order theoretic completeness conditions and what properties the norm in such a Banach lattice may possess and describe their centres. Various extension and separation results known for spaces of real-valued continuous functions are generalised to this setting