p-Fourier algebras on compact groups

2014/11/10 by Lee, Hun Hee, Samei, Ebrahim, Spronk, Nico
#43A77 #46B70 #46J10 #46L07 #47L25 #47L30 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Primary 43A30 #Secondary 43A75

paper · doi:10.48550/arxiv.1411.2336

Abstract

Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in \citeforrestss1. In the case p\not=2 we find that A^p(G)≅ A^p(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.

Related

• Some Beurling-Fourier algebras on compact groups are operator algebras
• Beurling-Fourier algebras, operator amenability and Arens regularity
• Beurling-Fourier algebras on compact groups: spectral theory
• Fourier algebra of a compact Lie group
• Beurling-Fourier algebras on Lie groups and their spectra