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

46E05Lattices of continuous, differentiable or analytic functions
46E40Spaces of vector- and operator-valued functions
Full Text: DOI EuDML
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[8] \cS. Alpay and Z. Ercan, “CD0(Q,E) and CD\omega (Q,E)-spaces as Banach lattices,” Positivity, vol. 4, no. 3, pp. 213-225, 2000. · Zbl 0973.46026 · doi:10.1023/A:1009878527795
[9] Z. Ercan, “A concrete description of CD0(K)-spaces as C(X)-spaces and its applications,” Proceedings of the American Mathematical Society, vol. 132, no. 6, pp. 1761-1763, 2004. · Zbl 1050.46022 · doi:10.1090/S0002-9939-03-07235-6