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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quasi-equivalence classes of normal representations for a separable $C^{\ast }$-algebra
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by Herbert Halpern PDF
Trans. Amer. Math. Soc. 203 (1975), 129-140 Request permission

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
  • © Copyright 1975 American Mathematical Society
  • 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