A Weierstrass approximation theorem for topological vector spaces
\textit{J. B. Prolla} and \textit{S. Machado} [Trans. Am. Math. Soc. 186(1973), 247-258 (1974; Zbl 0289.46024)] proved that if E and F are real locally convex Hausdorff spaces, then the polynomial operators of finite type are dense in C(E,F) equipped with the compact-open topology. In the paper the author proves the analogous results when E and F are not necessarily convex and: 1) E has a sequence of projections with the Grothendieck approximation property [\textit{H. H. Schaeffer}, Topological vector spaces (1972; Zbl 0217.160), pp. 108-115]; 2) F has a sequence with the Grothendieck approximation property.
scientific article; zbMATH DE number 3895601