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Der beschränkte Fall des gewichteten Approximationsproblems für vektorwertige Funktionen

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Abstract

Let W be a linear subspace of a weighted space of type CV(X,E) and an A-module (A being a subalgebra of C(X)). The weighted approximation problem, as formulated by L. Nachbin [12] in the case E =\(\mathbb{K}\) and for W⊂CVo(X), asks for a description of the closure of W. In its bounded case (see [12]) a general answer was given by W.H. Summers [20] for W⊂CVo(X) which is, under certain additional assumptions on X and V, also valid for W⊂CVo(X,E) as J.B. Prolla [15] had already proved. By extending the methods developed in [10] it is shown in this paper that these results can be generalized to arbitrary X,V and E, and moreover, that by considering compactifications of X similar solutions can be found for subspaces of CV(X,E). Applying them to a result of K.-D. Bierstedt [2] the approximation property of (certain subspaces of) CV(X) can be derived. As a further application tensor products of weighted spaces are investigated.

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  1. Arbeitsstelle Mathematik, Fachbereich 17 der GH Paderborn, Postfach 1621, D-479, Paderborn, Pohlweg, Germany

    Gert Kleinstück

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Kleinstück, G. Der beschränkte Fall des gewichteten Approximationsproblems für vektorwertige Funktionen. Manuscripta Math 17, 123–149 (1975). https://doi.org/10.1007/BF01154086

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  • DOI: https://doi.org/10.1007/BF01154086

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