Tracial states and representations of C*-algebras

Abstract

In this chapter we adapt a technique, borrowed from the theory of II1 factors, of juxtaposing the GNS Hilbert space structure associated with a tracial state and the C*-algebra structure to study reduced group C*-algebras. An emphasis is given to the C*-algebras associated to free products of groups. We give basic norm estimates for the elements of a group algebra and present basics of Powers groups and criteria for simplicity of reduced group C*-algebras. The chapter concludes with a study of normalizers of diffuse masas.