2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152463A. Van Daele introduced and investigated so-called algebraic quantum groups. We proved that such algebraic quantum groups give rise to C*-algebraic quantum groups in the sense of Masuda, Nakagami & Woronowicz. We prove in this paper that the analytic structure of these C*-algebraic quantum groups can be pulled down to the algebraic quantum group.LaTeX, 29 pagesFunctional AnalysisOperator AlgebrasQuantum Algebratext