Amenability and weak amenability of the Fourier algebra

By B. Forrest, Volker Runde. 2002

111 citations recorded by the source corpus.

Abstract.Let G be a locally compact group. We show that its Fourier algebra A(G) is amenable if and only if G has an abelian subgroup of finite index, and that its Fourier–Stieltjes algebra B(G) is amenable if and only if G has a compact, abelian subgroup of finite index. We then show that A(G) is weakly amenable if the component of the identity of G is abelian, and we prove some partial results towards the converse.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e034e639440c48a8553f2e1eeb223e531ea87663

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In Algebra and Number Theory

1. Dona Strauss
2. Anthony To-Ming Lau
3. H. Garth Dales
4. Matthew Daws

In Applied Mathematics

1. Matthew Daws
2. H. Garth Dales
3. Dona Strauss
4. Anthony To-Ming Lau

In Mathematical Physics

1. Dona Strauss
2. Anthony To-Ming Lau
3. H. Garth Dales
4. Matthew Daws
5. M. S. Monfared

Citations in the corpus

• Banach Algebras on Semigroups and on Their Compactifications (2010, background): “We remark that it is also shown in [48] that A(G) is weakly amenable if and only if the connected component of the identity in G is abelian.”
• On ϕ-amenability of Banach algebras (2008, background): “The authors are grateful to the referee for drawing their attention to papers [8] and [13] and for pointing out a number of misprints.”
• p-Operator spaces and Figà-Talamanca-Herz algebras (2006, background): “We remark that the original question of when A(G) is amenable as a Banach algebra was finally settled in [13], where it is shown that A(G) is amenable if and only if G has a finite-index abelian subgroup.”