2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168056We show that if R is a compact domain in the complex plane with two or more holes and an anticonformal involution onto itself (or equivalently a hyperelliptic Schottky double), then there is an operator T which has R as a spectral set, but does not dilate to a normal operator with spectrum on the boundary of R.Post-refereed versionFunctional Analysis47A20text