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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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Primitive ideals of $C^{\ast }$-algebras associated with transformation groups
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by Elliot C. Gootman PDF
Trans. Amer. Math. Soc. 170 (1972), 97-108 Request permission

Abstract:

We extend results of E. G. Effros and F. Hahn concerning their conjecture that if $(G,Z)$ is a second countable locally compact transformation group, with $G$ amenable, then every primitive ideal of the associated ${C^ \ast }$-algebra arises as the kernel of an irreducible representation induced from an isotropy subgroup. The conjecture is verified if all isotropy subgroups lie in the center of $G$ and either (a) the restriction of each unitary representation of $G$ to some open subgroup contains a one-dimensional subrepresentation, or (b) $G$ has an open abelian subgroup and orbit closures in $Z$ are compact and minimal.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 170 (1972), 97-108
  • MSC: Primary 22D25; Secondary 46L05
  • DOI: https://doi.org/10.1090/S0002-9947-1972-0302818-X
  • MathSciNet review: 0302818