Centralizers of Fourier algebra of an amenable group
HTML articles powered by AMS MathViewer
- by P. F. Renaud
- Proc. Amer. Math. Soc. 32 (1972), 539-542
- DOI: https://doi.org/10.1090/S0002-9939-1972-0293019-8
- PDF | Request permission
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
- A. Derighetti, Some results on the Fourier-Stieltjes algebra of a locally compact group, Comment. Math. Helv. 45 (1970), 219–228. MR 412735, DOI 10.1007/BF02567327
- Pierre Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964), 181–236 (French). MR 228628, DOI 10.24033/bsmf.1607
- Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto-London, 1969. MR 0251549
- 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 239002
- Walter Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Applied Mathematics, No. 12, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0152834
- J. G. Wendel, Left centralizers and isomorphisms of group algebras, Pacific J. Math. 2 (1952), 251–261. MR 49911, DOI 10.2140/pjm.1952.2.251
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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