2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79149This paper continues the study of spectral synthesis and the topologies $τ_{\infty}$ and $τ_r$ on the ideal space of a Banach algebra, concentrating particularly on the class of Haagerup tensor products of C$^*$-algebras. For this class, it is shown that spectral synthesis is equivalent to the Hausdorffness of $τ_{\infty}$. Under a weak extra condition, spectral synthesis is shown to be equivalent to the Hausdorffness of $τ_r$.27 pages plain tex; some explanations addedOperator AlgebrasFunctional Analysis46H10;46K50text