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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48 .

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The topology on the primitive ideal space of transformation group $C^{\ast }$-algebras and C.C.R. transformation group $C^{\ast }$-algebras
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by Dana P. Williams PDF
Trans. Amer. Math. Soc. 266 (1981), 335-359 Request permission

Abstract:

If $(G,\Omega )$ is a second countable transformation group and the stability groups are amenable then ${C^ \ast }(G,\Omega )$ is C.C.R. if and only if the orbits are closed and the stability groups are C.C.R. In addition, partial results relating closed orbits to C.C.R. algebras are obtained in the nonseparable case. In several cases, the topology of the primitive ideal space is calculated explicitly. In particular, if the stability groups are all contained in a fixed abelian subgroup $H$, then the topology is computed in terms of $H$ and the orbit structure, provided ${C^ \ast }(G,\Omega )$ and ${C^ \ast }(H,\Omega )$ are $EH$-regular. These conditions are automatically met if $G$ is abelian and $(G,\Omega )$ is second countable.
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Additional Information
  • © Copyright 1981 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 266 (1981), 335-359
  • MSC: Primary 46L05; Secondary 22D25, 54H15
  • DOI: https://doi.org/10.1090/S0002-9947-1981-0617538-7
  • MathSciNet review: 617538