Continuous mappings of a Banach space into a space
Let be a completely regular Hausdorff space, a real normed space, and let be the space of all bounded continuous -valued functions on . We develop the general duality theory of the space endowed with locally solid topologies; in particular with the strict topologies for . As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures for . It is shown that if a subset of is relatively -compact, then the set is still relatively -compact...
For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an -extender (resp. -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...
Soit un domaine borné strictement pseudoconvexe dans à frontière régulière . On montre que tout compact d’une sous-variété de dont l’espace tangent en chaque point de est contenu dans le sous-espace complexe maximal de est un ensemble pic pour , la classe des fonctions analytiques dans dont toutes les dérivées sont continues dans .