2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137149We study some reduced free products of C*-algebras with amalgamations. We give sufficient conditions for the positive cone of the K_0 group to be the largest possible. We also give sufficient conditions for simplicity and uniqueness of trace. We use the later result to give a necessary and sufficient condition for simplicity and uniqueness of trace of the reduced C*-algebras of the Baumslag-Solitar groups BS(m,n).23 pagesOperator AlgebrasFunctional Analysis46L09text