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Leinert sets and complemented ideals in Fourier algebras

Tom 239 / 2017

Michael Brannan, Brian Forrest, Cameron Zwarich 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.

Autorzy

  • Michael Brannan
  • Brian Forrest
  • Cameron Zwarich

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