2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169452Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain weak*-closed ideal in $H^\infty_B$ and use this to prove an analogue of the Nevanlinna-Pick interpolation theorem.19 pages, no figuresFunctional AnalysisOperator Algebras47A57; 46E22text