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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.
MSC:
43A30Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
43-02Research monographs (abstract harmonic analysis)
46H05General theory of topological algebras
46H20Structure and classification of topological algebras
46H25Normed modules and Banach modules, topological modules
46L07Operator spaces and completely bounded maps
47L25Operator spaces (= matricially normed spaces)