Leinert sets and complemented ideals in Fourier algebras
Tom 239 / 2017
Studia Mathematica 239 (2017), 273-296
MSC: Primary 43A15, 43A22; Secondary 46H10.
DOI: 10.4064/sm8733-3-2017
Opublikowany online: 26 March 2017
Streszczenie
We show how complemented ideals in the Fourier algebra of G arise naturally from a class of thin sets known as Leinert sets. Moreover, we present an explicit example of a closed ideal in A(\mathbb {F}_{N}), where \mathbb {F}_{N} is the free group on N \ge 2 generators, that is complemented in A(\mathbb {F}_{N}) but it is not completely complemented. Then by establishing an appropriate extension result for restriction algebras arising from Leinert sets, we show that any almost connected group G for which every complemented ideal in A(G) is also completely complemented must be amenable.