2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135367We study positivity in C*-modules and operator spaces using open tripotents, and an ordered version of the `noncommutative Shilov boundary'. Because of their independent interest, we also systematically study open tripotents and their properties.To appearOperator AlgebrasFunctional Analysistext