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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)].

##### MSC:
 4.6e+06 Lattices of continuous, differentiable or analytic functions 4.6e+41 Spaces of vector- and operator-valued functions
##### Keywords:
centre; Banach lattice; Alexandroff duplicate
Full Text:
##### References:
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