A theorem on weighted 𝐿¹-approximation

Schmidt, Darrell

doi:10.1090/S0002-9939-1987-0897074-4

A theorem on weighted $L^ 1$-approximation
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Proc. Amer. Math. Soc. 101 (1987), 81-84 Request permission

Abstract:

It is proven that the $A$-property is necessary for a finitedimensional subspace to be Chebyshev in $C(K)$ with respect to the weighted ${L^1}$-norm $||f|{|_w} = \int _K {w|f|d\mu }$ for all weight functions $w$ in certain classes of functions.

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