Order Structure of the Figà-Talamanca-Herz Algebra
نویسندگان
چکیده
منابع مشابه
Operator Figà-Talamanca–Herz algebras
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 ...
متن کاملOperator space structure and amenability for Figà-Talamanca–Herz algebras
Column and row operator spaces — which we denote by COL and ROW, respectively — over arbitrary Banach spaces were introduced by the first-named author; for Hilbert spaces, these definitions coincide with the usual ones. Given a locally compact group G and p, p ∈ (1,∞) with 1 p + 1 p = 1, we use the operator space structure on CB(COL(L ′ (G))) to equip the Figà-Talamanca–Herz algebra Ap(G) with ...
متن کاملp-Operator Spaces and Figà-Talamanca-Herz Algebras
We study a generalisation of operator spaces modelled on Lp spaces, instead of Hilbert spaces, using the notion of p-complete boundedness, as studied by Pisier and Le Merdy. We show that the Figà-Talamanca-Herz Algebras Ap(G) becomes quantised Banach algebras in this framework, and that the cohomological notion of amenability of these algebras corresponds to amenability of the locally compact g...
متن کاملFourier and Figà-Talamanca–Herz algebras on amenable, locally compact groups
For a locally compact group G, let A(G) denote its Fourier algebra and, for p ∈ (1,∞), let Ap(G) be the corresponding Figà-Talamanca–Herz algebra. For amenable G and p, p ∈ (1,∞) such that 1 p + 1 p , we show that Ap(G) ∩Ap′(G) = A(G).
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ژورنال
عنوان ژورنال: ISRN Geometry
سال: 2011
ISSN: 2090-6307,2090-6315
DOI: 10.5402/2011/531023