CQ *-algebras of measurable operators

Abstract

We study, from a quite general point of view, a CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms. Non-commutative L2-spaces are shown to constitute examples of a class of CQ*-algebras and any abstract CQ*-algebra (X, 𝖀0) possessing a sufficient family of bounded positive tracial sesquilinear forms can be represented as a direct sum of non-commutative L2-spaces.

Keywords

• banach c*-modules
• non commutative integration
• partial algebras of operators
• primary 46l08
• secondary 46l51, 47l60