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

YUHJTMAN, SERGIO A.

REVISTA DE LA UNIóN MATEMáTICA ARGENTINA

UNION MATEMATICA ARGENTINA

Lugar: Bahia Blanca; Año: 2015

0041-6932

We show that for any C*-algebra A, a sufficiently large Hilbert space Hand a unit vector \xi \in H, the natural application rep(A:H) \to Q(A),\pi \mapsto \langle \pi(-)\xi,\xi \rangle is a topological quotient, whererep(A:H) is the space of representations on H and Q(A) the set ofquasi-states, i.e. positive linear functionals with norm at most 1. Thisquotient might be a useful tool in the representation theory of C*-algebras. Weapply it to give an interesting proof of Takesaki-Bichteler duality forC*-algebras which allows to drop a hypothesis.