Beurling-Figà-Talamanca-Herz algebras

• Autorzy: Serap Öztop , Volker Runde , Nico Spronk
• Języki publikacji: 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.

Kategorie tematyczne

• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 46J10: Banach algebras of continuous functions, function algebras
• 43A32: Other transforms and operators of Fourier type
• 46H05: General theory of topological algebras
• 22D12: Other representations of locally compact groups
• 43A99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 210
• Numer: 2
• Strony: 117-135

Daty

wydano

2012

Twórcy

autor

Serap Öztop

• Department of Mathematics, Faculty of Science, Istanbul University, Istanbul, Turkey

autor

Volker Runde

• Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, Canada T6G 2G1

autor

Nico Spronk

• Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada N2L 3G1

Identyfikatory

DOI

10.4064/sm210-2-2