SIMULTANEOUS LIFTING FROM IRREDUCIBLE REPRESENTATIONS OF C*-ALGEBRAS

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