SciELO - Scientific Electronic Library Online

vol.38 issue3Upper triangular operator matrices and limit points of the essential spectrum author indexsubject indexarticles search
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • On index processCited by Google
  • Have no similar articlesSimilars in SciELO
  • On index processSimilars in Google


Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.38 no.3 Antofagasta Aug. 2019 


Interpolation and approximation from sublattices of C₀(X; R)

1 Universidade Federal de Itajubá, Instituto de Matemática e Computação - IMC. 37500-903 Itajubá, MG, Brasil. e-mail :


In this paper, we give a proof of a result concerning simultaneous interpolation and approximation from sublattices of the space of real continuous functions vanishing at infinity.

Keywords: Bonsall; Lattices; Interpolation; Approximation

Mathematics Subject Classification (2000): 41A65; 41A05

Texto completo disponible sólo en PDF.

Full text available only in PDF format.


The author acknowledges the referees for the valuable comments and suggestions.


[1] S. Boel, T. Carlsen and N. Hansen, "A Useful Strengthening of the Stone-Weierstrass Theorem", The American Mathematical Monthly, vol. 108, no. 7, p. 642, 2001, doi: 10.2307/2695271. [ Links ]

[2] F. Bonsall, "Semi-Algebras of Continuous Functions", Proceedings of the London Mathematical Society, vol. s3-10, no.1, pp. 122-140, 1960, doi: 10.1112/plms/s3-10.1.122. [ Links ]

[3] F. Deutsch, "Simultaneous Interpolation and Approximation in Topological Linear Spaces", SIAM Journal on Applied Mathematics, vol. 14, no. 5, pp. 1180-1190, 1966, doi: 10.1137/0114095. [ Links ]

[4] W. Rudin, Real and complex analysis, 3rd ed. Singapore: McGraw-Hill, 1987. [ Links ]

[5] G. Simmons, Introduction to topology and modern analysis. New York: McGraw-Hill, 1963. [ Links ]

[6] H. Wu, "New Stone-Weierstrass Theorem", Advances in Pure Mathematics, vol. 06, no. 13, pp. 943-947, 2016, doi: 10.4236/apm.2016.613071. [ Links ]

Received: April 2017; Accepted: May 2019

Creative Commons License This is an open-access article distributed under the terms of the Creative Commons Attribution License