Operator Figà-Talamanca–Herz algebras
نویسنده
چکیده
Let G be a locally compact group. We use the canonical operator space structure on the spaces L(G) for p ∈ [1,∞] introduced by G. Pisier to define operator space analoguesOAp(G) of the classical Figà-Talamanca–Herz algebrasAp(G). If p ∈ (1,∞) is arbitrary, then Ap(G) ⊂ OAp(G) such that the inclusion is a contraction; if p = 2, then OA2(G) ∼= A(G) as Banach spaces spaces, but not necessarily as operator spaces. We show that OAp(G) is a completely contractive Banach algebra for each p ∈ (1,∞), and that OAq(G) ⊂ OAp(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 OAp(G) for one (or equivalently for all) p ∈ (1,∞).
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