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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)].
MSC:
46E05Lattices of continuous, differentiable or analytic functions
46E40Spaces of vector- and operator-valued functions