Journal of Function Spaces

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Journal of Function Spaces / 2010 / Article

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Volume 8 |Article ID 645369 | 13 pages | https://doi.org/10.1155/2010/645369

On Hilbert extensions of Weierstrass' theorem with weights

Yamilet Quintana 1

1Departamento de Matemáticas, Puras y Aplicadas, Edificio Matemáticas y Sistemas (MYS), Apartado Postal: 89000, Caracas 1080 A, Universidad Simón Bolívar, Caracas, Venezuela

Academic Editor: Wilfredo Urbina
Received01 Apr 2006

Abstract

In this paper we study the set of ℊ-valued functions which can be approximated by ℊ-valued continuous functions in the norm Lℊ∞(I,w), where I⊂ℝ is a compact interval, ℊ is a separable real Hilbert space and w is a certain ℊ-valued weakly measurable weight. Thus, we obtain a new extension of the celebrated Weierstrass approximation theorem.

Copyright © 2010 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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