The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate

Abstract

We characterize the centre of the Banach lattice of Banach lattice $E$-valued continuous functions on the Alexandroff duplicate of a compact Hausdorff space $K$ in terms of the centre of $C(K,E)$, the space of $E$-valued continuous functions on $K$. We also identify the centre of $C{D}_{0}(Q,E)=C(Q,E)+{c}_{0}(Q,E)$ whose elements are the sums of $E$-valued continuous and discrete functions defined on a compact Hausdorff space $Q$ without isolated points, which was given by Alpay and Ercan (2000).