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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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Invariant states
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by Richard H. Herman PDF
Trans. Amer. Math. Soc. 158 (1971), 503-512 Request permission

Abstract:

States of a ${C^ \ast }$-algebra invariant under the action of a group of automorphisms of the ${C^ \ast }$-algebra are considered. It is shown that “clustering” states in the same part are equal and thus the same is true of extremal invariant states under suitable conditions. The central decomposition of an invariant state is considered and it is shown that the central measure is mixing if and only if the state satisfies a strong notion of clustering. Under transitivity of the central measure and some reasonable restrictions, the central decomposition is the ergodic decomposition of the state with respect to the isotropy subgroup.
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 158 (1971), 503-512
  • MSC: Primary 46.65
  • DOI: https://doi.org/10.1090/S0002-9947-1971-0281013-6
  • MathSciNet review: 0281013