Structural properties of some function spaces

Function bases for topological vector spaces

“…An analogous result for the Xvalued sequence space c 0 (X) = c 0 (N, X) was obtained earlier by J. Mendoza [11]. In [16], for a locally convex space X, we deal with the function spaces 1 (A, X) and c 0 (A, X) and study some geometric and structural properties such as the separability and linear functionals on them. Furthermore, in [17], we characterized the continuous operators from an arbitrary Banach spaces to the any of these spaces by introducing a new notation as relative adjoint operators.…”

The problem of isometric extension on the unit sphere of the space $ l\cap l^p(H)$ for $0 < p < 1$

“…Kadets and Martin in [6] proved that any surjective isometry between unit spheres of finite-dimensional polyhedral Banach spaces has a linear isometric extension to the whole space. See also [2,3,4,5,9,11,12] for some related results.…”

Some Properties of lp(A, X) Spaces

“…We say that x belongs to l p A, X if and only if investigated some structural properties of the function space l 1 A, X for a Hausdorff locally convex space X and obtained the continuous duals of l 1 A, X and c 0 A, X for a normed space X. It should be mentioned that 2 is a powerful tool in the detailed investigation of mentioned function spaces.…”