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 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).
Highlights
If K is a discrete topological space, C0 K, E is the space of E-valued bounded functions f on K such that the set k∈K:ε< f k
Cb∗ KΣ, Z E s denotes the set of all norm bounded and continuous functions f from K into Z E such that rαf kα e → rf k e in E for each e ∈ E whenever kα, rα → k, r in KΣ,Γ ⊗ {0, 1}
We consider the vector space Cb KΣ, Z E s × Cb∗ KΣ, Z E s equipped with coordinatewise algebraic operations, the order
Summary
If K is a discrete topological space, C0 K, E is the space of E-valued bounded functions f on K such that the set k∈K:ε< f k. The compact Hausdorff topology on K × {0, 1} generated by the open base A A1 ∪ A2, where When Γ is discrete topology on K, the compact Hausdorff topological space KΣ,Γ ⊗ {0, 1} will be denoted by A K .
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