JournalsprimsVol. 32 , No. 1DOI 10.2977/prims/1195163181

CQ*-Algebras: Structure Properties

  • Fabio Bagarello

    Università degli Studi di Palermo, Italy
  • Camillo Trapani

    Università degli Studi di Palermo, Italy
CQ*-Algebras: Structure Properties cover

Abstract

Some structure properties of CQ * -algebras are investigated. The usual multiplication of a quasi *-algebra is generalized by introducing a weak- and strong product. The *-semisemplicity is defined via a suitable family of positive sesquilinear forms and some consequences of this notion are derived. The basic elements of a functional calculus on these partial algebraic structures are discussed.