Approximate diagonals and Følner conditions for amenable group and semigroup algebras

Ross Stokke. "Approximate diagonals and Følner conditions for amenable group and semigroup algebras." Studia Mathematica 164.2 (2004): 139-159. <http://eudml.org/doc/284707>.

@article{RossStokke2004,
abstract = {We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally compact group G is amenable precisely when L¹(G) is an amenable Banach algebra. Several structural Følner-type conditions are derived, each of which is shown to correctly reflect the amenability of L¹(G). We provide Følner conditions characterizing semigroups with 1-amenable semigroup algebras.},
author = {Ross Stokke},
journal = {Studia Mathematica},
keywords = {locally compact group; group algebra; semigroup algebra; amenability; approximate diagonal; virtual diagonal; Følner conditions},
language = {eng},
number = {2},
pages = {139-159},
title = {Approximate diagonals and Følner conditions for amenable group and semigroup algebras},
url = {http://eudml.org/doc/284707},
volume = {164},
year = {2004},
}

TY - JOUR
AU - Ross Stokke
TI - Approximate diagonals and Følner conditions for amenable group and semigroup algebras
JO - Studia Mathematica
PY - 2004
VL - 164
IS - 2
SP - 139
EP - 159
AB - We study the relationship between the classical invariance properties of amenable locally compact groups G and the approximate diagonals possessed by their associated group algebras L¹(G). From the existence of a weak form of approximate diagonal for L¹(G) we provide a direct proof that G is amenable. Conversely, we give a formula for constructing a strong form of approximate diagonal for any amenable locally compact group. In particular we have a new proof of Johnson's Theorem: A locally compact group G is amenable precisely when L¹(G) is an amenable Banach algebra. Several structural Følner-type conditions are derived, each of which is shown to correctly reflect the amenability of L¹(G). We provide Følner conditions characterizing semigroups with 1-amenable semigroup algebras.
LA - eng
KW - locally compact group; group algebra; semigroup algebra; amenability; approximate diagonal; virtual diagonal; Følner conditions
UR - http://eudml.org/doc/284707
ER -