Publications of the Research Institute for Mathematical Sciences
Full-Text PDF (3756 KB) | Table of Contents | PRIMS summary
Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras
Jean-Pierre Antoine (1), Atsushi Inoue (2) and Camillo Trapani (3)(1) Institut de Physique Théorique, Université Catholique de Louvain, B-1348, LOUVAIN-LA-NEUVE, BELGIUM
(2) Department of Mathematics, Hiroshima University, 1-3-1 Kagamiyama, Higashi, 739-8526, HIROSHIMA, JAPAN
(3) Dipartimento di Matematica e Applicazioni, Università degli Studi di Palermo, v. Archirafi, 34, I-90123, 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.
No keywords available for this article.