On Representations of Partial *-Algebras Based on B\mathfrak B-Weights

  • Klaus-Detlef Kürsten

    Universität Leipzig, Germany
  • Elmar Wagner

    Universität Leipzig, Germany


A generalization of the GNSGNS-representation is investigated that represents partial *-algebras as systems of operators acting on a partial inner product space (i.e., PIPPIP-space). It is based on possibly indefinite B\mathfrak B-weights which are closely related to the positive B\mathfrak B-weights introduced by J.-P. Antoine, Y. Soulet and C. Trapani. Some additional assumptions had to be made in order to guarantee the GNSGNS-construction. Different partial products of operators on a PIPPIP-space are considered which allow the GNSGNS-construction under suitable conditions. Several examples illustrate the argumentation and indicate inherent problems.

Cite this article

Klaus-Detlef Kürsten, Elmar Wagner, On Representations of Partial *-Algebras Based on B\mathfrak B-Weights. Z. Anal. Anwend. 19 (2000), no. 3, pp. 623–638

DOI 10.4171/ZAA/971