un 2 00 0 On representations of partial ∗ - algebras based on B - weights
نویسنده
چکیده
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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ar X iv : m at h / 99 02 06 1 v 1 [ m at h . O A ] 9 F eb 1 99 9 On representations of partial ∗ - algebras based on B - weights
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-...
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