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• # Artykuł - szczegóły

## Studia Mathematica

2012 | 210 | 2 | 117-135

## Beurling-Figà-Talamanca-Herz algebras

EN

### Abstrakty

EN
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.

117-135

wydano
2012

### Twórcy

autor
• Department of Mathematics, Faculty of Science, Istanbul University, Istanbul, Turkey
autor
• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1
autor
• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1