On approximation in weighted spaces of continuous vector-valued functions
Copyright policy )On approximation in weighted spaces of continuous vector-valued functions
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.
- University of Benghazi Libyan Arab Jamahiriya
completely regular Hausdorff space, admissible space, Spaces of vector- and operator-valued functions, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), continuous vector-valued functions, Nachbin family, Hausdorff topological vector space, Topological linear spaces of continuous, differentiable or analytic functions, upper semi- continuous functions, locally bounded space, finite covering dimension
completely regular Hausdorff space, admissible space, Spaces of vector- and operator-valued functions, Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.), continuous vector-valued functions, Nachbin family, Hausdorff topological vector space, Topological linear spaces of continuous, differentiable or analytic functions, upper semi- continuous functions, locally bounded space, finite covering dimension
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