Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-15T10:20:03.905Z Has data issue: false hasContentIssue false
  • English
  • Français

On approximation in weighted spaces of continuous vector-valued functions

Published online by Cambridge University Press:  18 May 2009

Liaqat Ali Khan
Liaqat Ali Khan
Affiliation:
Department Of Mathematics, Faculty of Science, Garyounis University, P.O. Box 9480, Benghazi, Libya.
Rights & Permissions [Opens in a new window]

Extract

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.

The fundamental work on approximation in weighted spaces of continuous functions on a completely regular space has been done mainly by Nachbin ([5], [6]). Further investigations have been made by Summers [10], Prolla ([7], [8]), and other authors (see the monograph [8] for more references). These authors considered functions with range contained in the scalar field or a locally convex topological vector space. In the present paper we prove some approximation results without local convexity of the range space.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 1 , January 1987 , pp. 65 - 68
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

REFERENCES

1.Katsaras, A. K., On the strict topology in the non-locally convex setting, Math. Nachr. 102 (1981), 321–329.CrossRefGoogle Scholar
2.Khan, L. A., The strict topology on a space of vector-valued functions, Proc. Edinburgh Math. Soc. 22 (1979), 35–41.CrossRefGoogle Scholar
3.Klee, V., Shrinkable neighbourhoods in Hausdorff linear spaces, Math. Ann. 141 (1960), 281–285.CrossRefGoogle Scholar
4.Klee, V., Leray-Schauder theory without local convexity, Math. Ann. 141 (1960), 286–296.Google Scholar
5.Nachbin, L., Weighted approximation for algebras and. modules of continuous functions: real and self-adjoint complex cases, Ann. of Math. 81 (1965), 289–302.CrossRefGoogle Scholar
6.Nachbin, L., Elements of approximation theory, (van Nostrand, D., 1967).Google Scholar
7.Prolla, J. B., Bishop's generalized Stone-Weierstrass theorem for weighted spaces, Math. Ann. 191 (1971), 283–289.CrossRefGoogle Scholar
8.Prollas, J. B., Approximation of vector-valued functions, Mathematics Studies No. 25 (North-Holland, 1977).Google Scholar
9.Shuchat, A. H., Approximation of vector-valued continuous functions, Proc. Amer. Math. Soc. 31 (1972), 97–103.CrossRefGoogle Scholar
10.Summers, W. H., A general complex bounded case of the strict weighted approximation problem, Math. Ann. 192 (1971), 90–98.CrossRefGoogle Scholar