Loading...
Please wait, while we are loading the content...
Similar Documents
Operator Figà-Talamanca–Herz algebras (2001)
| Content Provider | CiteSeerX |
|---|---|
| Author | Runde, Volker |
| Abstract | 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 OAp(G) of the classical Figà-Talamanca–Herz algebras Ap(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, ∞). Keywords: amenability; complex interpolation; Figà-Talamanca–Herz algebra; Fourier algebra; locally compact groups; operator spaces; operator L p-spaces. |
| File Format | |
| Publisher Date | 2001-01-01 |
| Access Restriction | Open |
| Subject Keyword | Compact Group Complex Interpolation Operator P-spaces Canonical Operator Space Structure Fourier Algebra Operator Space Analogue Oap Operator Fig Talamanca Herz Algebra Classical Fig Talamanca Herz Fig Talamanca Herz Algebra Operator Space Bounded Approximate Identity Contractive Banach Algebra Banach Space Space |
| Content Type | Text |
