On ideals in the bidual of the Fourier algebra and related algebras
For a nonmetrizable compact group \(G\) whose local weight \(b(G)\) has uncountable cofinality and an amenable locally compact group \(H\), let \(A(G\times H)\) be the Fourier algebra of \(G\times H\) and \(UC_2(G\times H)\) be the space of uniformly continuous functionals in the group von Neumann algebra \(VN(G\times H)\) of \(G\times H\). In this paper, the authors show that there exist at least \(2^{2^{b(G)}}\) left ideals of dimensions at least \(2^{2^{b(G)}}\) in \(A(G\times H)^{**}\) and in \(UC_2(G\times H)^*\). It is also proved that every nontrivial right ideal in \(A(G\times H)^{**}\) and in \(UC_2(G\times H)^*\) has dimension at least \(2^{2^{b(G)}}\).
dual of uniformly continuous functionals
scientific article; zbMATH DE number 5708600
scientific article