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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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A generalized Powers averaging property for commutative crossed products
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by Tattwamasi Amrutam and Dan Ursu PDF
Trans. Amer. Math. Soc. 375 (2022), 2237-2254 Request permission


We prove a generalized version of Powers’ averaging property that characterizes simplicity of reduced crossed products $C(X) \rtimes _\lambda G$, where $G$ is a countable discrete group, and $X$ is a compact Hausdorff space which $G$ acts on minimally by homeomorphisms. As a consequence, we generalize results of Hartman and Kalantar on unique stationarity to the state space of $C(X) \rtimes _\lambda G$ and to Kawabe’s generalized space of amenable subgroups $\operatorname {Sub}_a(X,G)$. This further lets us generalize a result of the first named author and Kalantar on simplicity of intermediate C*-algebras. We prove that if $C(Y) \subseteq C(X)$ is an inclusion of unital commutative $G$-C*-algebras with $X$ minimal and $C(Y) \rtimes _\lambda G$ simple, then any intermediate C*-algebra $A$ satisfying $C(Y) \rtimes _\lambda G \subseteq A \subseteq C(X) \rtimes _\lambda G$ is simple.
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Additional Information
  • Tattwamasi Amrutam
  • Affiliation: Department of Mathematics, University of Houston, 3551 Cullen Blvd., Room 641, Philip Guthrie Hoffman Hall, Houston, Texas 77204-3008
  • Address at time of publication: Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 8410501, Israel
  • MR Author ID: 1407185
  • ORCID: 0000-0002-0691-5821
  • Email:
  • Dan Ursu
  • Affiliation: Department of Pure Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada
  • ORCID: 0000-0002-3235-4589
  • Email:
  • Received by editor(s): February 21, 2021
  • Received by editor(s) in revised form: June 28, 2021, and September 29, 2021
  • Published electronically: December 22, 2021
  • Additional Notes: The second author was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) [grant number PGSD3-535032-2019]. Deuxième auteur financé par le Conseil de recherches en sciences naturelles et en génie du Canada (CRSNG) [numéro de subvention PGSD3-535032-2019]
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 2237-2254
  • MSC (2020): Primary 37A55, 46L55, 46L89, 47L65
  • DOI:
  • MathSciNet review: 4378093