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...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/604931 |
| id |
doaj-155d0d46161648739fad7c55b2fd892c |
|---|---|
| record_format |
Article |
| spelling |
doaj-155d0d46161648739fad7c55b2fd892c2020-11-24T23:00:40ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Faruk Polat |
| spellingShingle |
Faruk Polat The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate Abstract and Applied Analysis |
| author_facet |
Faruk Polat |
| author_sort |
Faruk Polat |
| title |
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_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_sort |
centre of the spaces of banach lattice-valued continuous functions on the generalized alexandroff duplicate |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2011-01-01 |
| 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). |
| url |
http://dx.doi.org/10.1155/2011/604931 |
| work_keys_str_mv |
AT farukpolat thecentreofthespacesofbanachlatticevaluedcontinuousfunctionsonthegeneralizedalexandroffduplicate AT farukpolat centreofthespacesofbanachlatticevaluedcontinuousfunctionsonthegeneralizedalexandroffduplicate |
| _version_ |
1725641579692032000 |