Resumen de The quasi-state space of a C ∗ -algebra is a topological quotient of the representation space

Sergio A. Yuhjtman

• We show that for any C∗-algebra A, a sufficiently large Hilbert space H and a unit vector ξ∈H the natural application rep(A:H)→θξ−→(-), π↦⟨π(−)ξ,ξ⟩ is a topological quotient, where rep(A:H) is the space of representations on H and Q(A) the set of quasi-states, i.e. positive linear functionals with norm at most 1. This quotient might be a useful tool in the representation theory of C∗-algebras. We apply it to give an interesting proof of Takesaki–Bichteler duality for C∗-algebras which allows to drop a hypothesis.