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Quasi-equivalence classes of normal representations for a separable $ C\sp{\ast} $-algebra


Author: Herbert Halpern
Journal: Trans. Amer. Math. Soc. 203 (1975), 129-140
MSC: Primary 46L05
DOI: https://doi.org/10.1090/S0002-9947-1975-0367669-1
MathSciNet review: 0367669
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Abstract: It is shown that the set of quasi-equivalence classes of normal representations of a separable $ {C^\ast }$-algebra is a Borel subset of the quasi-dual with the Mackey Borel structure and forms a standard Borel space in the induced Borel structure. It is also shown that the set of factor states which induce normal representations forms a Borel set of the space of factor states with the $ {w^\ast }$-topology and that this set has a Borel transversal.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0367669-1
Keywords: Separable $ {C^\ast }$-algebras, quasi-dual, normal representations, trace representations, factor states, standard Borel space
Article copyright: © Copyright 1975 American Mathematical Society

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