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The general complex case of the Bernstein-Nachbin approximation problem. (English) Zbl 0365.41007

##### MSC:
 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 46E25 Rings and algebras of continuous, differentiable or analytic functions 30E10 Approximation in the complex plane
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##### References:
 [1] E. BISHOP, A generalization of the stone-Weierstrass theorem, Pacific J. Math., 11 (1961), 777-783. · Zbl 0104.09002 [2] I. GLICKSBERG, Measures orthogonal to algebras and sets of antisymmetry, Trans, Amer. Math. Soc., 105 (1962), 415-435. · Zbl 0111.11801 [3] R.I. JEWETT, A variation on the stone-Weierstrass theorem, Proc. Amer. Math. Soc., 14 (1963), 690-693. · Zbl 0122.35004 [4] G. KLEINSTUCK, Der beschränkte fall des gewichteten approximationsproblems für vektorwertige funktionen, Manuscripta Math., 17 (1975), 123-149. · Zbl 0343.41033 [5] L. NACHBIN, On the priority of algebras of continuous functions in weighted approximation, to appear in Symposia Mathematica. · Zbl 0338.41034 [6] L. NACHBIN, Elements of approximation theory, D. van Nostran Co., Inc., 1967. Reprinted by R. Krieger Co., Inc., 1976. · Zbl 0173.41403 [7] L. NACHBIN, S. MACHADO, and J.B. PROLLA, Weighted approximation, vector fibrations, and algebras of operators, Journal Math. Pures et appl., 50 (1971), 299-323. · Zbl 0238.46041 [8] J.B. PROLLA, Bishop’s generalized stone-Weierstrass theorem for weighted spaces, Math. Ann., 191 (1971), 283-289. · Zbl 0202.12603 [9] W. RUDIN, Real and complex analysis, McGraw-Hill, New York, 1966. · Zbl 0142.01701 [10] W.H. SUMMERS, Weighted approximation for modules of continuous functions II, in “Analyse fonctionnelle et applications” (Editor L. Nachbin), Hermann, Paris, 1975, p. 277-283. · Zbl 0321.41029
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