2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73092In an earlier paper, Dawson and the second author asked whether or not a Banach function algebra with dense invertible group can have a proper Shilov boundary. We give an example of a uniform algebra showing that this can happen, and investigate the properties of such algebras.11 pages, LaTeX, no figuresFunctional Analysis46J10text