Approximation by invertible functions of $H^{∞}$ - Nicolau, Artur; Suárez, Daniel (MATHEMATICA SCANDINAVICA, 2006)
We provide an analytic proof that if $H^∞$ is the algebra of bounded analytic functions on the unit disk, $A$ is a Banach algebra and $f: H^∞ → A$ is a Banach algebras morphism with dense image, then $f((H^∞)^{-1})$ is dense in $A^{-1}$.