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

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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.
Authors spelling K.-D. Kürsten, 16 pages, Latex. Changed formulation of Proposition 3.4

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Operator Algebras, 47D40 (Primary) 46C50, 46K10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/78084

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9902061
 http://arxiv.org/abs/math/9902061

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arXiv