Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Centralizers of Fourier algebra of an amenable group


Author: P. F. Renaud
Journal: Proc. Amer. Math. Soc. 32 (1972), 539-542
MSC: Primary 43A10
DOI: https://doi.org/10.1090/S0002-9939-1972-0293019-8
MathSciNet review: 0293019
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let G be a locally compact group with Fourier algebra $ A(G)$. We prove that if G is amenable then every centralizer of $ A(G)$ is determined by multiplication with an element of the Fourier-Stieltjes algebra of G. This result is then used to show that isometric centralizers correspond to characters of G.


References [Enhancements On Off] (What's this?)

  • [1] A. Derighetti, Some results on the Fourier-Stieltjes algebra of a locally compact group, Comment. Math. Helv. 45 (1970), 219–228. MR 0412735, https://doi.org/10.1007/BF02567327
  • [2] Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 0228628
  • [3] Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
  • [4] Horst Leptin, Sur l’algèbre de Fourier d’un groupe localement compact, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A1180–A1182 (French). MR 0239002
  • [5] Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley and Sons), New York-London, 1962. MR 0152834
  • [6] J. G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math. 2 (1952), 251–261. MR 0049911

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A10

Retrieve articles in all journals with MSC: 43A10


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0293019-8
Keywords: Locally compact group, amenable group, Fourier algebra, centralizer
Article copyright: © Copyright 1972 American Mathematical Society