2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78084A generalization of the GNS-representation is investigated that represents partial ^*-algebras as systems of operators acting on a partial inner product space (PIP-space). It is based on possibly indefinite B-weights which are closely related to the positive B-weights introduced by J.-P. Antoine, Y. Soulet and C. Trapani. Some additional assumptions had to be made in order to guarantee the GNS-construction. Different partial products of operators on a PIP-space are considered which allow the GNS-construction under suitable conditions. Several examples illustrate the argumentation and indicate inherent problems.Authors spelling K.-D. Kürsten, 16 pages, Latex. Changed formulation of Proposition 3.4Operator Algebras47D40 (Primary) 46C50, 46K10 (Secondary)text