JournalsprimsVol. 27 , No. 3DOI 10.2977/prims/1195169662

Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras

  • Jean-Pierre Antoine

    Université Catholique de Louvain, Louvain-La-Neuve, Belgium
  • Atsushi Inoue

    Hiroshima University, Japan
  • Camillo Trapani

    Università degli Studi di Palermo, Italy
Partial *-Algebras of Closable Operators. II. States and Representations of Partial *-Algebras cover

Abstract

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.