The Oka-Weil theorem in topological vector spaces

• Autorzy: Bui Dac Tac
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 32E30: Holomorphic and polynomial approximation, Runge pairs, interpolation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 3
• Strony: 255-262

Daty

wydano

1991

otrzymano

1988-11-05

poprawiono

1989-08-03

Twórcy

autor

Bui Dac Tac

• Department of Mathematics, Pedagogical Institute 1, Hanoi, Vietnam

Bibliografia

• [1] R. M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976), 7-30.
• [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.
• [3] A. Bayoumi, Bounding subsets of some metric vector spaces, Ark. Mat. 18 (1980), 13-17.
• [4] A. Martineau, Sur une propriété caractéristique d'un produit de droites, Arch. Math. (Basel) 11 (1960), 423-426.
• [5] C. Matyszczyk, Approximation of analytic and continuous mappings by polynomials in Fréchet spaces, Studia Math. 60 (1977), 223-238.
• [6] P. L. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland Math. Stud. 3, Amsterdam 1973.