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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Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/604931 |
| 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 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). |
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| ISSN: | 1085-3375 1687-0409 |