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 CD(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).