In this talk we will go further into the study of representations of C-star algebras. In particular we will talk about Naimark's problem, which asks whether every C-star algebra with only one irreducible representation (up to unitary equivalence) is necessarily the algebra of compact operators on some Hilbert space. Although the answer is yes in some special cases (eg, when the C-star algebra is separable), we will sketch the construction of a counterexample (from Akemann and Weaver, 2004) using diamond.

Notes on this series of talks