On Hilbert extensions of Weierstrass' theorem with weights

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In this paper we study the set of functions $\GG$-valued which can be approximated by $\GG$-valued continuous functions in the norm $L^\infty_{\GG}(I,w)$, where $I$ is a compact interval, $\GG$ is a real and separable Hilbert space and $w$ is certain $\GG$-valued weakly measurable weight. Thus, we obtain a new extension of celebrated Weierstrass approximation theorem.
Corrected version, 14 pages

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Classical Analysis and ODEs, Functional Analysis, 41, 41A10, 43A32, 47A56

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http://salesiana.dossiersoluciones.com/handle/123456789/160434

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0611034
 http://arxiv.org/abs/math/0611034

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arXiv