Quasi-equivalence classes of normal representations for a separable 𝐶*-algebra

Halpern, Herbert

doi:10.1090/S0002-9947-1975-0367669-1

Quasi-equivalence classes of normal representations for a separable $C^{\ast }$-algebra
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by Herbert Halpern

Trans. Amer. Math. Soc. 203 (1975), 129-140

DOI: https://doi.org/10.1090/S0002-9947-1975-0367669-1

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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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