Approximations from Subspaces of C0(X)
We show among other things that if B is a linear space of continuous real-valued functions vanishing at infinity on a locally compact Hausdorff space X, for which there is a continuous function h defined in a neighbourhood of 0 in the real line which is non-affine in every neighbourhood of 0 and sat...
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| Published in | Journal of approximation theory Vol. 112; no. 2; pp. 279 - 294 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
01.10.2001
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| Online Access | Get full text |
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| Summary: | We show among other things that if B is a linear space of continuous real-valued functions vanishing at infinity on a locally compact Hausdorff space X, for which there is a continuous function h defined in a neighbourhood of 0 in the real line which is non-affine in every neighbourhood of 0 and satisfies |h(t)|⩽k|t| for all t, such that hb is in B whenever b is in B and the composite function is defined, then every function in C0(X) which can be approximated on every pair of points in X by functions in B can be approximated uniformly by functions in B. |
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| ISSN: | 0021-9045 1096-0430 |
| DOI: | 10.1006/jath.2001.3596 |