Biweights and *-homomorphisms of partial *-algebras

Consider two partial *-algebras, 1 and 2, and an *-homomorphism Φ from 1 into 2. Given a biweight ϕ on 2, we discuss conditions under which the natural composition ϕ∘Φ of ϕ and Φ is a biweight on 1. In particular, we examine whether the restriction of a biweight to a partial *-subalgebra is again a biweight.

A note on Banach partial *-algebras