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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Projections in $L^1(G)$: the unimodular case
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by Mahmood Alaghmandan, Mahya Ghandehari, Nico Spronk and Keith F. Taylor PDF
Proc. Amer. Math. Soc. 144 (2016), 4929-4941 Request permission


We consider the issue of describing all self-adjoint idempotents (projections) in $L^1(G)$ when $G$ is a unimodular locally compact group. The approach is to take advantage of known facts concerning subspaces of the Fourier-Stieltjes and Fourier algebras of $G$ and the topology of the dual space of $G$. We obtain an explicit description of any projection in $L^1(G)$ which happens to also lie in the coefficient space of a finite direct sum of irreducible representations. This leads to a complete description of all projections in $L^1(G)$ for $G$ belonging to a class of groups that includes $\textrm {SL}_2({\mathbb R})$ and all second countable almost connected nilpotent locally compact groups.
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Additional Information
  • Mahmood Alaghmandan
  • Affiliation: Department of Mathematical Sciences, Chalmers University of Technology and the University of Gothenburg, S-412 96 Göteborg, Sweden
  • Email:
  • Mahya Ghandehari
  • Affiliation: Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716
  • MR Author ID: 741919
  • Email:
  • Nico Spronk
  • Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
  • MR Author ID: 671665
  • Email:
  • Keith F. Taylor
  • Affiliation: Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada B3H 3J5
  • MR Author ID: 171225
  • Email:
  • Received by editor(s): October 21, 2015
  • Received by editor(s) in revised form: January 22, 2016
  • Published electronically: April 27, 2016
  • Additional Notes: The first two authors were supported by Fields Institute postdoctoral fellowships and postdoctoral fellowships at the University of Waterloo. The second author was supported by an AARMS postdoctoral fellowship while at Dalhousie University. The third and fourth authors were supported by NSERC of Canada Discovery Grants.
  • Communicated by: Pamela Gorkin
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 4929-4941
  • MSC (2010): Primary 43A20; Secondary 43A22
  • DOI:
  • MathSciNet review: 3544540