Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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.
Słowa kluczowe
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)
Czasopismo
Rocznik
Tom
Numer
Strony
365-383
Opis fizyczny
Daty
wydano
2010
Twórcy
autor
- Department of Pure Mathematics, University of Waterloo, 200 University Ave. W., Waterloo, Ontario, N2L 3G1, Canada
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-22