Simultaneous Lifting From Irreducible Representations of $C^*$ -Algebras

Abstract

Abstract. Given a sequence (π n ) of irreducible representations of a liminal C * -algebra A, and a sequence (b n ) of trace class operators with b n ∈ π n (A), we investigate necessary conditions and sufficient conditions for the existence of a simultaneous lifting a ∈ A such that, for each n, the trace of σ (a) is bounded for irreducible representations σ in a neighbourhood of π n .