p -Fourier algebras on compact groups
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Hun Hee Lee [1] ; Ebrahim Samei [2] ; Nico Spronk [3]
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[1] Seoul National University
Seoul National University
Corea del Sur
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[2] University of Saskatchewan
University of Saskatchewan
Canadá
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[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
- DOI: 10.4171/rmi/1033
- Texto completo no disponible (Saber más ...)
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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.
