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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Chebyshev rank in $ L\sb 1$-approximation

Author: András Kroó
Journal: Trans. Amer. Math. Soc. 296 (1986), 301-313
MSC: Primary 41A52; Secondary 41A65
MathSciNet review: 837813
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Abstract: Let $ {C_\omega }(K)$ denote the space of continuous functions endowed with the norm $ {\smallint _K}\omega \left\vert f \right\vert = {\left\Vert f \right\Vert _\omega },\omega > 0$. In this paper we characterize the subspaces $ {U_n} \subset {C_\omega }(K)$ having Chebyshev rank at most $ k\;(0 \leq k \leq n - 1)$ with respect to all bounded positive weights $ \omega $. Various applications of main results are also presented.

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PII: S 0002-9947(1986)0837813-5
Article copyright: © Copyright 1986 American Mathematical Society