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Duality theory of spaces of vector-valued continuous functions

Marian Nowak, Aleksandra Rzepka (2005)

Commentationes Mathematicae Universitatis Carolinae

Let X be a completely regular Hausdorff space, E a real normed space, and let C b ( X , E ) be the space of all bounded continuous E -valued functions on X . We develop the general duality theory of the space C b ( X , E ) endowed with locally solid topologies; in particular with the strict topologies β z ( X , E ) for z = σ , τ , t . As an application, we consider criteria for relative weak-star compactness in the spaces of vector measures M z ( X , E ' ) for z = σ , τ , t . It is shown that if a subset H of M z ( X , E ' ) is relatively σ ( M z ( X , E ' ) , C b ( X , E ) ) -compact, then the set conv ( S ( H ) ) is still relatively σ ( M z ( X , E ' ) , C b ( X , E ) ) -compact...

Dugundji extenders and retracts on generalized ordered spaces

Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)

Fundamenta Mathematicae

For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an L c h -extender (resp. L c c h -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 L c h -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology and...

Ensembles pics pour A ( D )

Jacques Chaumat, Anne-Marie Chollet (1979)

Annales de l'institut Fourier

Soit D un domaine borné strictement pseudoconvexe dans C n à frontière régulière D . On montre que tout compact d’une sous-variété N de D dont l’espace tangent T p ( N ) en chaque point p de N est contenu dans le sous-espace complexe maximal de T p ( D ) est un ensemble pic pour A ( D ) , la classe des fonctions analytiques dans D dont toutes les dérivées sont continues dans D .

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