Studenterkollokvium: C*-algebras and the GNS construction

SPEAKER: Andreas Hallbäck

TITLE: C*-algebras and the GNS construction

ABSTRACT: 
This will be an introduction to C*-algebras. We will give both the abstract algebraic definition and the concrete definition as a sub-algebra of the bounded operators on a Hilbert space. The aim of the talk is to show that these two definitions are equivalent, i.e. that they define the same objects up to isomorphism. This is the so-called GNS construction and a sketch of the proof will be given. The talk is meant as a preliminary talk to a seminar on the 23rd of March about the classification of C*-algebras by means of descriptive set theory. The attendants are assumed to be acquainted with Hilbert space theory.