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

• Autorzy: Nico Spronk
• Języki publikacji: EN

Abstrakty

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.

Kategorie tematyczne

• 46J20: Ideals, maximal ideals, boundaries
• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46L07: Operator spaces and completely bounded maps
• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 43A07: Means on groups, semigroups, etc.; amenable groups
• 43A77: Analysis on general compact groups
• 43A85: Analysis on homogeneous spaces
• 22D10: Unitary representations of locally compact groups
• 43A20: L 1 -algebras on groups, semigroups, etc.
• 43A10: Measure algebras on groups, semigroups, etc.
• 43-02: Research exposition (monographs, survey articles)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 365-383

Daty

wydano

2010

Twórcy

autor

Nico Spronk

• Department of Pure Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, Ontario, N2L 3G1, Canada

Identyfikatory

DOI

10.4064/bc91-0-22