Resumen de p -Fourier algebras on compact groups

Hun Hee Lee, Ebrahim Samei, Nico Spronk

• 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.