Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey. (English) Zbl 1209.43004
Loy, Richard J. (ed.) et al., Banach algebras 2009. Proceedings of the 19th international conference, Bȩdlewo, Poland, July 14–24, 2009. Warszawa: Polish Academy of Sciences, Institute of Mathematics (ISBN 978-83-86806-10-2/pbk). Banach Center Publications 91, 365-383 (2010).
The author gives a survey of various Banach algebraic amenability properties – most notably: amenability, weak amenability, and biflatness – for the Fourier algebra and the Fourier-Stieltjes algebra of a locally compact group. He also focuses on variants of these properties that take the natural operator space structure of those Banach algebras into account.
|43A30||Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.|
|43-02||Research monographs (abstract harmonic analysis)|
|46H05||General theory of topological algebras|
|46H20||Structure and classification of topological algebras|
|46H25||Normed modules and Banach modules, topological modules|
|46L07||Operator spaces and completely bounded maps|
|47L25||Operator spaces (= matricially normed spaces)|