On representations of partial ^*-algebras based on B-weights
Operator Algebras
2007-05-23 v2
Abstract
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.
Keywords
Cite
@article{arxiv.math/9902061,
title = {On representations of partial ^*-algebras based on B-weights},
author = {Klaus-Detlef Kuersten and Elmar Wagner},
journal= {arXiv preprint arXiv:math/9902061},
year = {2007}
}
Comments
Authors spelling K.-D. K\"ursten, 16 pages, Latex. Changed formulation of Proposition 3.4