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

Abstract

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