The quasi-state space of a C*-algebra is a topological quotient of the representation space

摘要

We show that for any C -algebra A, a su ciently large Hilbertspace H and a unit vector 2 H, the natural application rep(A:H) ????! Q(A), 7! h (??) ; i is a topological quotient, where rep(A:H) is the space ofrepresentations on H and Q(A) the set of quasi-states, i.e. positive linearfunctionals with norm at most 1. This quotient might be a useful tool inthe representation theory of C -algebras. We apply it to give an interestingproof of Takesaki{Bichteler duality for C -algebras which allows to drop ahypothesis.