Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras
Jean-Pierre AntoineUniversité Catholique de Louvain, Louvain-La-Neuve, Belgium
Atsushi InoueHiroshima University, Japan
Camillo TrapaniUniversità degli Studi di Palermo, Italy
This second paper on partial Op*-algebras is devoted to the theory of representations. A new definition of invariant positive sesquilinear forms on partial *-algebras is proposed, which enables to perform the familiar GNS construction. In order to get a better control of the corresponding representations, we introduce and study a restricted class of partial Op*-algebras, called partial GW*-algebras, which turn up naturally in a number of problems. As an example, we extend Powers' results about the standardness of GNS representations of abelian partial *-algebras.
Cite this article
Jean-Pierre Antoine, Atsushi Inoue, Camillo Trapani, Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras. Publ. Res. Inst. Math. Sci. 27 (1991), no. 3, pp. 399–430DOI 10.2977/PRIMS/1195169662