GNS Construction for C^*-Valued Positive Sesquilinear Maps on a quasi *-algebra

The GNS construction for positive invariant sesquilinear forms on quasi *-algebra ( A, A₀) ( A , A 0 ) is generalized to a class of positive sesquilinear maps from A× A A × A into a C^* C ∗ -algebra C C . The result is a *-representation taking values in a space of operators acting on a certain quasi-normed C C -module.