-Fourier algebras on compact groups

  • Hun Hee Lee

    Seoul National University, Republic of Korea
  • Ebrahim Samei

    University of Saskatchewan, Saskatoon, Canada
  • Nico Spronk

    University of Waterloo, Canada

Abstract

Let be a compact group. For we introduce a class of Banach function algebras on which are the Fourier algebras in the case , and for are certain algebras discovered by Forrest, Samei and Spronk. In the case we find that if and only if and are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call -Beurling–Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie and , our techniques of estimation of when certain -Beurling–Fourier algebras are operator algebras rely more on the fine structure of , than in the case . We also study restrictions to subgroups. In the case that SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.

Cite this article

Hun Hee Lee, Ebrahim Samei, Nico Spronk, -Fourier algebras on compact groups. Rev. Mat. Iberoam. 34 (2018), no. 4, pp. 1469–1514

DOI 10.4171/RMI/1033