2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/99270We construct three different families of commuting pairs of subnormal operators, jointly hyponormal but not admitting commuting normal extensions. Each such family can be used to answer in the negative a 1988 conjecture of R. Curto, P. Muhly and J. Xia. We also obtain a sufficient condition under which joint hyponormality does imply joint subnormality.20 pages, 7 figuresFunctional AnalysisPrimary 47B20, 47B37, 47A13, 28A50; Secondary 44A60, 47-04, 47A20text