Structural properties of some function spaces Original Research Article

Ferrando and Lüdkovsky (J. Math. Anal. Appl. 274 (2002) 577–585), have investigated some structral properties of the function space c0(A,X)c0(A,X) for a Hausdorff locally convex space X. In this work, we are mainly interested in the space ℓ(A,X)ℓ(A,X) of all unordered absolute summable functions from a set A into a Hausdorff locally convex space X. The main result of the work is the representation of the elements of ℓ(A,X)ℓ(A,X) and c0(A,X).c0(A,X). These representations are related with the separability of the spaces and provide us to obtain continuous duals of ℓ(A,X)ℓ(A,X) and c0(A,X)c0(A,X) for a normed space X.X. This improves the Ferrando and Lüdkovskyʹs investigation with geometric aspects.