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Zbl 1221.46025
Polat, Faruk
The centre of the spaces of Banach lattice-valued continuous functions on the generalized Alexandroff duplicate. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 604931, 5 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

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 2000:: *46E05 Lattices of functions defined by smoothness properties
46E40 Spaces of vector-valued functions

Keywords: centre; Banach lattice; Alexandroff duplicate

Citations: Zbl 0973.46026

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