Chebyshev rank in 𝐿₁-approximation

Kroó, András

doi:10.1090/S0002-9947-1986-0837813-5

Chebyshev rank in $L_ 1$-approximation
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Trans. Amer. Math. Soc. 296 (1986), 301-313 Request permission

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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