Sur certaines extensions du théorème d'approximation de Bernstein
Let X be a compact space and A a closed subalgebra of C(X). The real functions in A define closed equivalence classes in X. A theorem of Silov states that a continuous function f is in A if and only if the restriction of f to each equivalence class is in the space of restrictions of elements of A. Bishop obtained an improved version of this result. In the present paper, generalizations of these results of Silov and Bishop are obtained in which firstly A is replaced by a vector subspace E of C(X). In turn E is replaced by a cone of functions with values in a real or complex Banach space.
scientific article; zbMATH DE number 3919002