Beurling-Figà-Talamanca-Herz algebras

Serap Öztop, Volker Runde, and Nico Spronk. "Beurling-Figà-Talamanca-Herz algebras." Studia Mathematica 210.2 (2012): 117-135. <http://eudml.org/doc/285581>.

@article{SerapÖztop2012,
abstract = {For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_\{p\}(G,ω)$. For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that a locally compact group G is amenable if and only if one-and, equivalently, every-Beurling-Figà-Talamanca-Herz algebra $A_\{p\}(G,ω)$ has a bounded approximate identity.},
author = {Serap Öztop, Volker Runde, Nico Spronk},
journal = {Studia Mathematica},
keywords = {weight; Beurling algebra; Fourier algebra; Figà-Talamanca-Herz algebra; p-operator space; amenable group},
language = {eng},
number = {2},
pages = {117-135},
title = {Beurling-Figà-Talamanca-Herz algebras},
url = {http://eudml.org/doc/285581},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Serap Öztop
AU - Volker Runde
AU - Nico Spronk
TI - Beurling-Figà-Talamanca-Herz algebras
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 2
SP - 117
EP - 135
AB - For a locally compact group G and p ∈ (1,∞), we define and study the Beurling-Figà-Talamanca-Herz algebras $A_{p}(G,ω)$. For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group Ĝ. For p = 2 and compact G, our approach subsumes an earlier one by H. H. Lee and E. Samei. The key to our approach is not to define Beurling algebras through weights, i.e., possibly unbounded continuous functions, but rather through their inverses, which are bounded continuous functions. We prove that a locally compact group G is amenable if and only if one-and, equivalently, every-Beurling-Figà-Talamanca-Herz algebra $A_{p}(G,ω)$ has a bounded approximate identity.
LA - eng
KW - weight; Beurling algebra; Fourier algebra; Figà-Talamanca-Herz algebra; p-operator space; amenable group
UR - http://eudml.org/doc/285581
ER -