The centre of the spaces of Banach lattice-valued continuous functions on the generalized Alexandroff duplicate (Q535974)

Summary: 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 \textit{S. Alpay} and \textit{Z. Ercan} [Positivity 4, No. 3, 213--225 (2000; Zbl 0973.46026)].