The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate
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 𝐶𝐷0(𝑄,𝐸)=𝐶(𝑄,𝐸)+𝑐0(𝑄,𝐸) whose...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/604931 |
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| author | Faruk Polat |
| author_facet | Faruk Polat |
| author_sort | Faruk Polat |
| collection | DOAJ |
| description | 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 𝐶𝐷0(𝑄,𝐸)=𝐶(𝑄,𝐸)+𝑐0(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 Alpay and Ercan (2000). |
| format | Article |
| id | doaj-art-155d0d46161648739fad7c55b2fd892c |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-155d0d46161648739fad7c55b2fd892c2025-08-20T02:02:40ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/604931604931The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff DuplicateFaruk Polat0Department of Mathematics, Firat University, 23119 Elazig, TurkeyWe 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 𝐶𝐷0(𝑄,𝐸)=𝐶(𝑄,𝐸)+𝑐0(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 Alpay and Ercan (2000).http://dx.doi.org/10.1155/2011/604931 |
| spellingShingle | Faruk Polat The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate Abstract and Applied Analysis |
| title | The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate |
| title_full | The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate |
| title_fullStr | The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate |
| title_full_unstemmed | The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate |
| title_short | The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate |
| title_sort | centre of the spaces of banach lattice valued continuous functions on the generalized alexandroff duplicate |
| url | http://dx.doi.org/10.1155/2011/604931 |
| work_keys_str_mv | AT farukpolat thecentreofthespacesofbanachlatticevaluedcontinuousfunctionsonthegeneralizedalexandroffduplicate AT farukpolat centreofthespacesofbanachlatticevaluedcontinuousfunctionsonthegeneralizedalexandroffduplicate |