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The centre of the spaces of Banach lattice-valued continuous functions on the generalized Alexandroff duplicate. (English) Zbl 1221.46025
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 S. Alpay and Z. Ercan [Positivity 4, No. 3, 213–225 (2000; Zbl 0973.46026)].

46E05 Lattices of continuous, differentiable or analytic functions
46E40 Spaces of vector- and operator-valued functions
Full Text: DOI EuDML
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