Convolutions on compact groups and Fourier algebras of coset spaces

• Autorzy: Brian E. Forrest , Ebrahim Samei , Nico Spronk
• Języki publikacji: EN

Abstrakty

EN

We study two related questions. (1) For a compact group G, what are the ranges of the convolution maps on A(G × G) given for u,v in A(G) by u × v ↦ u*v̌ (v̌(s) = v(s^-1)) and u × v ↦ u*v? (2) For a locally compact group G and a compact subgroup K, what are the amenability properties of the Fourier algebra of the coset space A(G/K)? The algebra A(G/K) was defined and studied by the first named author.
In answering the first question, we obtain, for compact groups which do not admit an abelian subgroup of finite index, some new subalgebras of A(G). Using those algebras we can find many instances in which A(G/K) fails the most rudimentary amenability property: operator weak amenability. However, using different techniques, we show that if the connected component of the identity of G is abelian, then A(G/K) always satisfies the stronger property that it is hyper-Tauberian, which is a concept developed by the second named author. We also establish a criterion which characterises operator amenability of A(G/K) for a class of groups which includes the maximally almost periodic groups. Underlying our calculations are some refined techniques for studying spectral synthesis properties of sets for Fourier algebras. We even find new sets of synthesis and nonsynthesis for Fourier algebras of some classes of groups.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 43A77: Analysis on general compact groups
• 47L25: Operator spaces (= matricially normed spaces)
• 43A85: Analysis on homogeneous spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 196
• Numer: 3
• Strony: 223-249

Daty

wydano

2010

Twórcy

autor

Brian E. Forrest

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada

autor

Ebrahim Samei

• Department of Mathematics & Statistics, University of Saskatchewan, Saskatoon, SK S7N 5E6, Canada

autor

Nico Spronk

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Identyfikatory

DOI

10.4064/sm196-3-2