Some approximation results for function spaces

AbstractLet X be a compact Hausdorff space and let A be a closed linear subspace of CC(X) containing constants and separating points of X. If D is a self-adjoint subalgebra of CC(X) then we characterize the uniform closure of the polynomials in D with coefficients in A in terms of the restriction of A to the sets of constancy for D, and we deduce some approximation results for functions of a complex variable. A theorem of Stone-Weierstrass type for complex simplex spaces is also proved