%0 Journal Article
%T On representations of partial ^*-algebras based on B-weights
%A Klaus-Detlef Kuersten
%A Elmar Wagner
%J Mathematics
%D 1999
%I arXiv
%X A 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.
%U http://arxiv.org/abs/math/9902061v2