The Oka-Weil theorem in topological vector spaces

Bui Dac Tac

Annales Polonici Mathematici (1991)

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

Abstract

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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.

How to cite

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Bui 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

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  1. [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. [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. [3] A. Bayoumi, Bounding subsets of some metric vector spaces, Ark. Mat. 18 (1980), 13-17. Zbl0443.46029
  4. [4] A. Martineau, Sur une propriété caractéristique d'un produit de droites, Arch. Math. (Basel) 11 (1960), 423-426. Zbl0099.31501
  5. [5] C. Matyszczyk, Approximation of analytic and continuous mappings by polynomials in Fréchet spaces, Studia Math. 60 (1977), 223-238. Zbl0357.46016
  6. [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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