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## Banach Center Publications

2010 | 91 | 1 | 365-383
Tytuł artykułu

### Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey

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EN
Let G be a locally compact group, and let A(G) and B(G) denote its Fourier and Fourier-Stieltjes algebras. These algebras are dual objects of the group and measure algebras, $L^{-1}(G)$ and M(G), in a sense which generalizes the Pontryagin duality theorem on abelian groups. We wish to consider the amenability properties of A(G) and B(G) and compare them to such properties for $L^{-1}(G)$ and M(G). For us, "amenability properties" refers to amenability, weak amenability, and biflatness, as well as some properties which are more suited to special settings, such as the hyper-Tauberian property for semisimple commutative Banach algebras. We wish to emphasize that the theory of operator spaces and completely bounded maps plays an indispensable role when studying A(G) and B(G). We also show some applications of amenability theory to problems of complemented ideals and homomorphisms.
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Tom
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365-383
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wydano
2010
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autor
• Department of Pure Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, Ontario, N2L 3G1, Canada
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