×

zbMATH — the first resource for mathematics

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:
46E05 Lattices of continuous, differentiable or analytic functions
46E40 Spaces of vector- and operator-valued functions
PDF BibTeX XML Cite
Full Text: DOI EuDML
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’AcadĂ©mie 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.