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

Copyright © 2006 Jean-Pierre Antoine et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.