Beurling-Figa-Talamanca-Herz algebras

Oztop S., Runde V., Spronk N.

STUDIA MATHEMATICA, cilt.210, sa.2, ss.117-135, 2012 (SCI-Expanded) identifier identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 210 Sayı: 2
  • Basım Tarihi: 2012
  • Doi Numarası: 10.4064/sm210-2-2
  • Dergi Adı: STUDIA MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.117-135
  • İstanbul Üniversitesi Adresli: Evet

Özet

For a locally compact group G and p is an element of (1, infinity), we define and study the Beurling-Figa-Talamanca-Herz algebras A(p)(G, omega). For p = 2 and abelian G, these are precisely the Beurling algebras on the dual group (G) over cap. 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-Figa-Talamanca-Herz algebra A(p)(G, omega) has a bounded approximate identity.