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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:
 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
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##### References:
 [1] C. D. Aliprantis and O. Burkinshaw, Positive Operators, Springer, Dordrecht, The Netherlands, 2006. · Zbl 1156.46001 [2] P. Meyer-Nieberg, Banach Lattices, Universitext, Springer, Berlin, Germany, 1991. · Zbl 0743.46015 [3] Z. Ercan and A. W. Wickstead, “Banach lattices of continuous Banach lattice-valued functions,” Journal of Mathematical Analysis and Applications, vol. 198, no. 1, pp. 121-136, 1996. · Zbl 0869.46012 · doi:10.1006/jmaa.1996.0072 [4] M. \cCaglar, Z. Ercan, and F. Polat, “Generalized Alexandroff duplicates and CD0(K) spaces,” Central European Journal of Mathematics, vol. 4, no. 3, pp. 371-375, 2006. · Zbl 1139.46032 · doi:10.2478/s11533-006-0018-5 [5] R. Engelking, “On the double circumference of Alexandroff,” Bulletin de l’Académie Polonaise des Sciences, vol. 16, pp. 629-634, 1968. · Zbl 0167.21001 [6] P. S. Alexandroff and P. S. Urysohn, “Memoire sur les espaces topologiques compacts,” Koninklijke Nederlandse Akademie van Wetenschappen te Amsterdam, vol. 14, pp. 1-96, 1929. · JFM 55.0960.02 [7] Y. A. Abramovich and A. W. Wickstead, “Remarkable classes of unital AM-spaces,” Journal of Mathematical Analysis and Applications, vol. 180, no. 2, pp. 398-411, 1993. · Zbl 0792.46004 · doi:10.1006/jmaa.1993.1408 [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
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