Best Approximation in Certain Douglas Algebras
Rahman M. Younis · Proceedings of the American Mathematical Society · 1980
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.