# Beurling-Figà-Talamanca-Herz algebras

Serap Öztop; Volker Runde; Nico Spronk

Studia Mathematica (2012)

- Volume: 210, Issue: 2, page 117-135
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topSerap 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.