Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T14:27:18.681Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Stone-Weierstrass theorem

Published online by Cambridge University Press:  09 April 2009

Kung-Fu Ng
Kung-Fu Ng
Affiliation:
Department of Mathematics, United College The Chinese University of Hong Kong.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let M be a vector subspace of the Banach space C(Ω) of all real-valued continuous functions on a compact space Ω, and suppose that M contains a subset L and the constant functions. Then in order that L be dense in M it is necessary and sufficient that L, M satisfy a filtering property and that each m in M can be approximated on every two points of Ω by functions in L.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 337 - 340
Copyright
Copyright © Australian Mathematical Society 1976

References

Alfsen, E. M. (1971), ‘Compact convex sets and boundary integrals’, Springer-Verlag.CrossRefGoogle Scholar
Bishop, E. and de Leeuw, K. (1959), ‘The presentation of linear functionals by measures on sets of extreme points’, Ann. Inst. Fourier (Grenoble) 9, 305–331.Google Scholar
Edwards, D. A. and Vincent-Smith, G. (1968), ‘A Weierstrass-Stone theorem for Choquet simplexes’, Ann. Inst. Fourier (Grenoble) 18, 261–282.Google Scholar
Edwards, D. A. (1969), ‘On uniform approximations of affine functions on compact convex sets’, Oxford Quarterly J. 20, 139–142.Google Scholar