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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Best $ L\sb 1$-approximation with varying weights


Author: András Kroó
Journal: Proc. Amer. Math. Soc. 99 (1987), 66-70
MSC: Primary 41A52; Secondary 41A65
MathSciNet review: 866431
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Abstract: It is proved in this note that the so-called $ A$-property is necessary in order that the finite-dimensional space $ U$ be Chebyshev in $ C\left( K \right)$ with respect to the norm $ \left\Vert f \right\Vert = \int_K {\omega \left\vert f \right\vert} $ for every positive continuous weight $ \omega $. It is also shown that for each finite-dimensional subspace $ U$ there exists a positive continuous weight $ \omega $ such that $ U$ is Chebyshev in $ C\left( K \right)$ with respect to this weight $ \omega $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0866431-4
PII: S 0002-9939(1987)0866431-4
Article copyright: © Copyright 1987 American Mathematical Society