p -Fourier algebras on compact groups

• Hun Hee Lee ^[1] ; Ebrahim Samei ^[2] ; Nico Spronk ^[3]
  1. [1] Seoul National University

     Seoul National University

     Corea del Sur

     
  2. [2] University of Saskatchewan

     University of Saskatchewan

     Canadá

     
  3. [3] University of Waterloo

     University of Waterloo

     Canadá

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 4, 2018, págs. 1469-1514
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let G be a compact group. For 1≤p≤∞ we introduce a class of Banach function algebras Ap(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered by Forrest, Samei and Spronk. In the case p≠2 we find that Ap(G)≅Ap(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling–Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p>1, our techniques of estimation of when certain p-Beurling–Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G= SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.