Geodesic
On weak approximation and convexification in weighted spaces of vector-valued continuous functions
Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 59-64

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a completely regular Hausdorff space. A Nachbin family of weights is a set V of upper-semicontinuous positive functions on X such that if u, υ ∈ V then there exists w ∈ V and t > 0 so that u, υ ≤ tw. For any Hausdorff topological vector space E, the weighted space CV0(X, E) is the space of all E-valued continuous functions f on X such that υf vanishes at infinity for all υ ∈ V. CV0(X, E) is equipped with the weighted topologywv = wv(X, E) which has as a base of neighbourhoods of zero the family of all sets of the formwhere υ ∈ Vand W is a neighbourhood of zero in E. If E is the scalar field, then the space CV0(X, E) is denoted by CV0(X). The reader is referred to [4, 6, 8] for information on weighted spaces. 
Nawrocki, Marek. On weak approximation and convexification in weighted spaces of vector-valued continuous functions. Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 59-64. doi: 10.1017/S0017089500007540
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[1] 1.Gillman, L. and Jerison, M., Rings of continuous functions, (Van Nostrand, 1960). Google Scholar | DOI

[2] 2.Kalton, N. J., Isomorphisms between spaces of vector-valued continuous functions, Proc. Edinburgh Math. Soc. 26 (1983), 29–48. Google Scholar | DOI

[3] 3.Katsaras, A. K., On the strict topology in non-locally convex setting, Math. Nachr. 102 (1981), 321–329. Google Scholar | DOI

[4] 4.Khan, L. A., On approximation in weighted spaces of continuous vector-valued functions, Glasgow Math. J. 29 (1987), 65–68. Google Scholar | DOI

[5] 5.Klee, V., Leray-Schauder theory without local convexity, Math. Ann. 141 (1960), 286–296. Google Scholar | DOI

[6] 6.Nachbin, L., Elements of approximation theory, (Van Nostrand, 1967). Google Scholar

[7] 7.Nawrocki, M., Strict dual of C b(X, E), Studio Math. 82 (1985), 33–38. Google Scholar | DOI

[8] 8.Prolla, J. B., Approximation of vector-valued functions, Mathematics Studies No. 25 (North-Holland, 1977). Google Scholar

[9] 9.Schuchat, A. H., Approximation of vector-valued continuous functions, Proc. Amer. Math. Soc. 31 (1972), 97–103. Google Scholar | DOI

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