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

• Sergio A. Yuhjtman ^[1]
  1. [1] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 56, Nº. 2, 2015, págs. 57-65
• Idioma: inglés
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• Resumen

  • 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.