Operator Figà-Talamanca-Herz algebras

• Autorzy: Volker Runde
• Języki publikacji: EN

Abstrakty

EN

Let G be a locally compact group. We use the canonical operator space structure on the spaces $L^{p}(G)$ for p ∈ [1,∞] introduced by G. Pisier to define operator space analogues $OA_{p}(G)$ of the classical Figà-Talamanca-Herz algebras $A_{p}(G)$. If p ∈ (1,∞) is arbitrary, then $A_{p}(G) ⊂ OA_{p}(G)$ and the inclusion is a contraction; if p = 2, then OA₂(G) ≅ A(G) as Banach spaces, but not necessarily as operator spaces. We show that $OA_{p}(G)$ is a completely contractive Banach algebra for each p ∈ (1,∞), and that $OA_{q}(G) ⊂ OA_{p}(G)$ completely contractively for amenable G if 1 < p ≤ q ≤ 2 or 2 ≤ q ≤ p < ∞. Finally, we characterize the amenability of G through the existence of a bounded approximate identity in $OA_{p}(G)$ for one (or equivalently for all) p ∈ (1,∞).

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 43A15: L p -spaces and other function spaces on groups, semigroups, etc.
• 46L07: Operator spaces and completely bounded maps
• 46B70: Interpolation between normed linear spaces
• 47L25: Operator spaces (= matricially normed spaces)
• 46J99: None of the above, but in this section

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2003
• Tom: 155
• Numer: 2
• Strony: 153-170

Daty

wydano

2003

Twórcy

autor

Volker Runde

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

Identyfikatory

DOI

10.4064/sm155-2-5