# The Oka-Weil theorem in topological vector spaces

Annales Polonici Mathematici (1991)

- Volume: 54, Issue: 3, page 255-262
- ISSN: 0066-2216

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topBui Dac Tac. "The Oka-Weil theorem in topological vector spaces." Annales Polonici Mathematici 54.3 (1991): 255-262. <http://eudml.org/doc/262455>.

@article{BuiDacTac1991,

abstract = {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.},

author = {Bui Dac Tac},

journal = {Annales Polonici Mathematici},

keywords = {strong polynomial approximation property; SPAP; WSPAP; pseudo-homogeneous seminorm; sequentially complete topological vector space; Schauder basis; bounded approximation property; BAP; continuous norm},

language = {eng},

number = {3},

pages = {255-262},

title = {The Oka-Weil theorem in topological vector spaces},

url = {http://eudml.org/doc/262455},

volume = {54},

year = {1991},

}

TY - JOUR

AU - Bui Dac Tac

TI - The Oka-Weil theorem in topological vector spaces

JO - Annales Polonici Mathematici

PY - 1991

VL - 54

IS - 3

SP - 255

EP - 262

AB - 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.

LA - eng

KW - strong polynomial approximation property; SPAP; WSPAP; pseudo-homogeneous seminorm; sequentially complete topological vector space; Schauder basis; bounded approximation property; BAP; continuous norm

UR - http://eudml.org/doc/262455

ER -

## References

top- [1] R. M. Aron and M. Schottenloher, Compact holomorphic mappings on Banach spaces and the approximation property, J. Funct. Anal. 21 (1976), 7-30. Zbl0328.46046
- [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. Zbl0443.46029
- [4] A. Martineau, Sur une propriété caractéristique d'un produit de droites, Arch. Math. (Basel) 11 (1960), 423-426. Zbl0099.31501
- [5] C. Matyszczyk, Approximation of analytic and continuous mappings by polynomials in Fréchet spaces, Studia Math. 60 (1977), 223-238. Zbl0357.46016
- [6] P. L. Noverraz, Pseudo-convexité, Convexité Polynomiale et Domaines d'Holomorphie en Dimension Infinie, North-Holland Math. Stud. 3, Amsterdam 1973. Zbl0251.46049

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