Let G be 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).

Amenable groups, Cancellable sets, Compact nonmetrizable groups, Double dual of Fourier algebra, Dual of uniformly continuous functionals, Factorization, Group von Neumann algebra, One-sided ideals, Unitary representations
dx.doi.org/10.1016/j.jfa.2009.12.011
Journal of Functional Analysis
School of Mathematics and Statistics

Filali, M., Neufang, M, & Sangani Monfared, M. (2010). On ideals in the bidual of the Fourier algebra and related algebras. Journal of Functional Analysis, 258(9), 3117–3133. doi:10.1016/j.jfa.2009.12.011