Order continuous operators on CD0(K, E) and CDw(K, E)-spaces

Abstract

In [2], Alpay and Ercan characterized order continuous duals of spaces CD0(K E) and CDw(K, E) where K is a compact Hausdorff space without isolated points and E is a Banach lattice. In this note, we generalize their results to an arbitrary Dedekind complete Banach lattice F, that is to say, we characterize order continuous operators on these spaces taking values in an arbitrary Dedekind complete Banach lattice F.