It is shown that a sequentially complete topological vector space X with a compact Schauder basis has WSPAP (see Definition 2) if and only if X has a pseudo-homogeneous norm bounded on every compact subset of X.
@article{bwmeta1.element.bwnjournal-article-apmv54z3p255bwm, author = {Bui Dac Tac}, title = {The Oka-Weil theorem in topological vector spaces}, journal = {Annales Polonici Mathematici}, volume = {55}, year = {1991}, pages = {255-262}, zbl = {0736.46043}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p255bwm} }
Bui Dac Tac. The Oka-Weil theorem in topological vector spaces. Annales Polonici Mathematici, Tome 55 (1991) pp. 255-262. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p255bwm/
[000] [1] R. M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976), 7-30. | Zbl 0328.46046
[001] [2] A. Bayoumi, The Levi problem and the radius of convergence of holomorphic functions on metric vector spaces, in: Lecture Notes in Math. 834, Springer, 1981, 9-32.
[002] [3] A. Bayoumi, Bounding subsets of some metric vector spaces, Ark. Mat. 18 (1980), 13-17. | Zbl 0443.46029
[003] [4] A. Martineau, Sur une propriété caractéristique d'un produit de droites, Arch. Math. (Basel) 11 (1960), 423-426. | Zbl 0099.31501
[004] [5] C. Matyszczyk, Approximation of analytic and continuous mappings by polynomials in Fréchet spaces, Studia Math. 60 (1977), 223-238. | Zbl 0357.46016
[005] [6] P. L. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland Math. Stud. 3, Amsterdam 1973. | Zbl 0251.46049