Quasi *-algebras of measurable operators

Abstract

Non-commutative Lp-spaces are shown to constitute examples of a class of Banach quasi *-algebras called CQ*-algebras. For p 2 they are also proved to possess a su cient family of bounded positive sesquilinear forms satisfying certain invariance properties. CQ *-algebras of measurable operators over a nite von Neumann algebra are also constructed and it is proven that any abstract CQ*-algebra (X;A0) possessing a su cient family of bounded positive tracial sesquilinear forms can be represented as a CQ*-algebra of this type.