Abstract and Applied Analysis
Volume 2011 (2011), Article ID 604931, 5 pages
doi:10.1155/2011/604931
Research Article

The Centre of the Spaces of Banach Lattice-Valued Continuous Functions on the Generalized Alexandroff Duplicate

Department of Mathematics, Firat University, 23119 Elazig, Turkey

Received 12 December 2010; Accepted 13 February 2011

Academic Editor: Yong Zhou

Copyright © 2011 Faruk Polat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 𝐶 𝐷 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 Alpay and Ercan (2000).