On ideals in the bidual of the Fourier algebra and related algebras
Journal of Functional Analysis , Volume 258 - Issue 9 p. 3117- 3133
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|
|Journal of Functional Analysis|
|Organisation||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