On representations of partial ^*-algebras based on B-weights

Details On representations of partial ^*-algebras based on B-weights On representations of partial ^*-algebras based on B-weights

1999-02-09

arxiv.org/abs/math/9902061v2

Mathematics

Operator Algebras

Authors spelling K.-D. K\"ursten, 16 pages, Latex. Changed formulation of Proposition 3.4

Scientific paper

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.

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