Order continuous operators on $CD _0$(K,E) and $CD _omega$(K,E)-spaces

Abstract

In [2], Alpay and Ercan characterized order continuous duals of spaces $CD _0$(K,E)and $CD _omega$(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 .