2010/07/27 by Nico Spronk, Spronk, Nico
Mathematics · #22D10 #43A10 #43A20 #43A30 #43A77 #43A85 #46H25 #46J20 #46L07 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary 43-02 #Secondary 43A07
paper · pdf · doi:10.48550/arxiv.1007.4804
openalex publication_date 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a locally compact group, and let A(G) and B(G) denote its Fourier\nand Fourier-Stieltjes algebras. These algebras are dual objects of the group\nand measure algebras, L1(G) and M(G), in a sense which generalizes the\nPontryagin duality theorem on abelian groups. We wish to consider the\namenability properties of A(G) and B(G) and compare them to such properties for\nL1(G) and M(G). For us, ``amenability properties'' refers to amenability, weak\namenability, and biflatness, as well as some properties which are more suited\nto special settings, such as the hyper-Tauberian property for semisimple\ncommutative Banach algebras. We wish to emphasize that the theory of operator\nspaces and completely bounded maps plays an indispensable role when studying\nA(G) and B(G). We also show some applications of amenability theory to problems\nof complemented ideals and homomorphisms.\n