International Journal of Mathematics and Mathematical Sciences 
Volume 2006 (2006), Article ID 54793, 20 pages
doi:10.1155/IJMMS/2006/54793

Biweights and *-homomorphisms of partial *-algebras

Jean-Pierre Antoine,1 Camillo Trapani,2 and Francesco Tschinke3

 1Institut de Physique Théorique, Université Catholique de Louvain, Louvain-la-Neuve 1348, Belgium
2Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo 90123, Italy
3Dipartimento di Metodi e Modelli Matematici, Facoltà d'Ingegneria, Università di Palermo, Palermo 90128, Italy
Received 26 May 2006; Revised 14 August 2006; Accepted 21 August 2006

Abstract

Consider two partial *-algebras, 𝔄1 and 𝔄2, and an *-homomorphism Φ from 𝔄1 into 𝔄2. Given a biweight ϕ on 𝔄2, we discuss conditions under which the natural composition ϕ∘Φ of ϕ and Φ is a biweight on 𝔄1. In particular, we examine whether the restriction of a biweight to a partial *-subalgebra is again a biweight.