Biweights and \(^{\ast}\)-homomorphisms of partial \(^{\ast}\)-algebras (Q933855)

Biweights on partial \(*\)-algebras allow a GNS construction and thus permit to develop from there a representation theory for partial \(*\)-algebras. Nevertheless, biweights exhibit unfamiliar features: the restriction of a biweight on a partial \(*\)-subalgebra is not necessarily a biweight. The authors present sufficient conditions under which \(\varphi\circ\Phi\) is a biweight on \({\mathfrak A}_1\), where \(\Phi\) is a \(*\)-homomorphism from a partial \(*\)-algebra \({\mathfrak A}_1\) to a partial \(*\)-algebra \({\mathfrak A}_2\) and \(\varphi\) is a biweight on \({\mathfrak A}_2\). Furthermore, they investigate the continuity of a \(*\)-homomorphism from a normed partial \(*\)-algebra to another one, making use of unbounded \(C^*\)-seminorms defined by biweights.