Best approximation in certain Douglas algebras

Younis, Rahman

doi:10.1090/S0002-9939-1980-0587943-0

Best approximation in certain Douglas algebras
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by Rahman Younis

Proc. Amer. Math. Soc. 80 (1980), 639-642

DOI: https://doi.org/10.1090/S0002-9939-1980-0587943-0

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Abstract:

The main result of this paper is that if $f \in {L^\infty }$ and S is a weak peak set for ${H^\infty }$, then the distance from f to the Douglas algebra $\{ f \in {L^\infty }:f{|_S} \in {H^\infty }{|_S}\}$ is attained.

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