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

Nico Spronk. "Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey." Banach Center Publications 91.1 (2010): 365-383. <http://eudml.org/doc/282309>.

@article{NicoSpronk2010,
abstract = {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.},
author = {Nico Spronk},
journal = {Banach Center Publications},
keywords = {amenability; Fourier algebra; Fourier-Stieltjes algebra; operator spaces},
language = {eng},
number = {1},
pages = {365-383},
title = {Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey},
url = {http://eudml.org/doc/282309},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Nico Spronk
TI - Amenability properties of Fourier algebras and Fourier-Stieltjes algebras: a survey
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 365
EP - 383
AB - 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.
LA - eng
KW - amenability; Fourier algebra; Fourier-Stieltjes algebra; operator spaces
UR - http://eudml.org/doc/282309
ER -