On ideals in the bidual of the Fourier algebra and related algebras

LetGbe a compact nonmetrizable topological group whose local weight b(G) has uncountable cofinality. Let H be an amenable locally compact group, A(G×H) the Fourier algebra of G×H, and UC2(G×H) the space of uniformly continuous functionals in VN(G×H) = A(G×H)∗. We use weak factorization of operators in the group von Neumann algebra VN(G× H) to prove that there exist at least 22b(G) left ideals of dimensions at least 22b(G) in A(G × H)∗∗ and in UC2(G × H)∗. We show that every nontrivial right ideal in A(G×H)∗∗ and in UC2(G×H)∗ has dimension at least 22b(G) . © 2010 Elsevier Inc. All rights reserved.