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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Chebyshev rank in $L_ 1$-approximation


Author: András Kroó
Journal: Trans. Amer. Math. Soc. 296 (1986), 301-313
MSC: Primary 41A52; Secondary 41A65
DOI: https://doi.org/10.1090/S0002-9947-1986-0837813-5
MathSciNet review: 837813
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Abstract: Let ${C_\omega }(K)$ denote the space of continuous functions endowed with the norm ${\smallint _K}\omega \left | f \right | = {\left \| f \right \|_\omega },\omega > 0$. 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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Article copyright: © Copyright 1986 American Mathematical Society