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 𝐶𝐷0(𝑄,𝐸)=𝐶(𝑄,𝐸)+𝑐0(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).