2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152384For partial automorphisms of $C^*$-algebras, Takai-Takesaki crossed product duality tends to fail, in proportion to the extent to which the partial automorphism is not an automorphism.18 pages, AMS-LaTeXFunctional AnalysisOperator AlgebrasCrossed product duality for partial $C^*$-automorphismstext